The Hall effect is the production of a potential difference (the Hall voltage ) across an electrical conductor that is transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current. It was discovered by Edwin Hall in 1879.
165-434: The Hall coefficient is defined as the ratio of the induced electric field to the product of the current density and the applied magnetic field. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of the charge carriers that constitute the current. Wires carrying current in a magnetic field experience a mechanical force perpendicular to both
330-869: A , {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\iint _{S}\,\sigma (\mathbf {r} '){\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}da,} and for line charges with linear charge density λ ( r ′ ) {\displaystyle \lambda (\mathbf {r} ')} on line L {\displaystyle L} E ( r ) = 1 4 π ε 0 ∫ L λ ( r ′ ) r ′ | r ′ | 3 d ℓ . {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\int _{L}\,\lambda (\mathbf {r} '){\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}d\ell .} If
495-869: A , {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\iint _{S}\,\sigma (\mathbf {r} '){\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}da,} and for line charges with linear charge density λ ( r ′ ) {\displaystyle \lambda (\mathbf {r} ')} on line L {\displaystyle L} E ( r ) = 1 4 π ε 0 ∫ L λ ( r ′ ) r ′ | r ′ | 3 d ℓ . {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\int _{L}\,\lambda (\mathbf {r} '){\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}d\ell .} If
660-557: A y -axis electrical force due to the buildup of charges. The v x term is the drift velocity of the current which is assumed at this point to be holes by convention. The v x B z term is negative in the y -axis direction by the right hand rule. F = q ( E + v × B ) {\displaystyle \mathbf {F} =q{\bigl (}\mathbf {E} +\mathbf {v} \times \mathbf {B} {\bigl )}} In steady state, F = 0 , so 0 = E y − v x B z , where E y
825-531: A Gaussian surface in this region that violates Gauss's law . Another technical difficulty that supports this is that charged particles travelling faster than or equal to speed of light no longer have a unique retarded time. Since electric field lines are continuous, an electromagnetic pulse of radiation is generated that connects at the boundary of this disturbance travelling outwards at the speed of light . In general, any accelerating point charge radiates electromagnetic waves however, non-radiating acceleration
990-531: A Gaussian surface in this region that violates Gauss's law . Another technical difficulty that supports this is that charged particles travelling faster than or equal to speed of light no longer have a unique retarded time. Since electric field lines are continuous, an electromagnetic pulse of radiation is generated that connects at the boundary of this disturbance travelling outwards at the speed of light . In general, any accelerating point charge radiates electromagnetic waves however, non-radiating acceleration
1155-420: A vector field . The electric field acts between two charges similarly to the way that the gravitational field acts between two masses , as they both obey an inverse-square law with distance. This is the basis for Coulomb's law , which states that, for stationary charges, the electric field varies with the source charge and varies inversely with the square of the distance from the source. This means that if
1320-414: A voltage (potential difference) between them; it is only an approximation because of boundary effects (near the edge of the planes, the electric field is distorted because the plane does not continue). Assuming infinite planes, the magnitude of the electric field E is: E = − Δ V d , {\displaystyle E=-{\frac {\Delta V}{d}},} where Δ V
1485-414: A voltage (potential difference) between them; it is only an approximation because of boundary effects (near the edge of the planes, the electric field is distorted because the plane does not continue). Assuming infinite planes, the magnitude of the electric field E is: E = − Δ V d , {\displaystyle E=-{\frac {\Delta V}{d}},} where Δ V
1650-398: A Hall effect consistent with positive carriers was observed in evidently n-type semiconductors. Another source of artefact, in uniform materials, occurs when the sample's aspect ratio is not long enough: the full Hall voltage only develops far away from the current-introducing contacts, since at the contacts the transverse voltage is shorted out to zero. When a current-carrying semiconductor
1815-670: A charge density ρ ( r ) = q δ ( r − r 0 ) {\displaystyle \rho (\mathbf {r} )=q\delta (\mathbf {r} -\mathbf {r} _{0})} , where the Dirac delta function (in three dimensions) is used. Conversely, a charge distribution can be approximated by many small point charges. Electrostatic fields are electric fields that do not change with time. Such fields are present when systems of charged matter are stationary, or when electric currents are unchanging. In that case, Coulomb's law fully describes
SECTION 10
#17328522456091980-623: A charge density ρ ( r ) = q δ ( r − r 0 ) {\displaystyle \rho (\mathbf {r} )=q\delta (\mathbf {r} -\mathbf {r} _{0})} , where the Dirac delta function (in three dimensions) is used. Conversely, a charge distribution can be approximated by many small point charges. Electrostatic fields are electric fields that do not change with time. Such fields are present when systems of charged matter are stationary, or when electric currents are unchanging. In that case, Coulomb's law fully describes
2145-651: A circular disc, subjected to a magnetic field perpendicular to the plane of the disc, produces a "circular" current through the disc. The absence of the free transverse boundaries renders the interpretation of the Corbino effect simpler than that of the Hall effect. Electric field An electric field (sometimes called E-field ) is the physical field that surrounds electrically charged particles . Charged particles exert attractive forces on each other when their charges are opposite, and repulse each other when their charges are
2310-428: A co-moving reference frame. Special theory of relativity imposes the principle of locality , that requires cause and effect to be time-like separated events where the causal efficacy does not travel faster than the speed of light . Maxwell's laws are found to confirm to this view since the general solutions of fields are given in terms of retarded time which indicate that electromagnetic disturbances travel at
2475-428: A co-moving reference frame. Special theory of relativity imposes the principle of locality , that requires cause and effect to be time-like separated events where the causal efficacy does not travel faster than the speed of light . Maxwell's laws are found to confirm to this view since the general solutions of fields are given in terms of retarded time which indicate that electromagnetic disturbances travel at
2640-415: A component of a unified electromagnetic field . The study of magnetic and electric fields that change over time is called electrodynamics . Electric fields are caused by electric charges , described by Gauss's law , and time varying magnetic fields , described by Faraday's law of induction . Together, these laws are enough to define the behavior of the electric field. However, since the magnetic field
2805-409: A magnetic field with a perpendicular component is applied, their paths between collisions are curved; thus, moving charges accumulate on one face of the material. This leaves equal and opposite charges exposed on the other face, where there is a scarcity of mobile charges. The result is an asymmetric distribution of charge density across the Hall element, arising from a force that is perpendicular to both
2970-476: A negative voltage on the left as shown in the diagram. Thus for the same current and magnetic field, the electric polarity of the Hall voltage is dependent on the internal nature of the conductor and is useful to elucidate its inner workings. This property of the Hall effect offered the first real proof that electric currents in most metals are carried by moving electrons, not by protons. It also showed that in some substances (especially p-type semiconductors ), it
3135-1312: A particle with electric charge q 1 {\displaystyle q_{1}} at position r 1 {\displaystyle \mathbf {r} _{1}} exerts a force on a particle with charge q 0 {\displaystyle q_{0}} at position r 0 {\displaystyle \mathbf {r} _{0}} of: F 01 = q 1 q 0 4 π ε 0 r ^ 01 | r 01 | 2 = q 1 q 0 4 π ε 0 r 01 | r 01 | 3 {\displaystyle \mathbf {F} _{01}={\frac {q_{1}q_{0}}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}_{01} \over {|\mathbf {r} _{01}|}^{2}}={\frac {q_{1}q_{0}}{4\pi \varepsilon _{0}}}{\mathbf {r} _{01} \over {|\mathbf {r} _{01}|}^{3}}} where Note that ε 0 {\displaystyle \varepsilon _{0}} must be replaced with ε {\displaystyle \varepsilon } , permittivity , when charges are in non-empty media. When
3300-1312: A particle with electric charge q 1 {\displaystyle q_{1}} at position r 1 {\displaystyle \mathbf {r} _{1}} exerts a force on a particle with charge q 0 {\displaystyle q_{0}} at position r 0 {\displaystyle \mathbf {r} _{0}} of: F 01 = q 1 q 0 4 π ε 0 r ^ 01 | r 01 | 2 = q 1 q 0 4 π ε 0 r 01 | r 01 | 3 {\displaystyle \mathbf {F} _{01}={\frac {q_{1}q_{0}}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}_{01} \over {|\mathbf {r} _{01}|}^{2}}={\frac {q_{1}q_{0}}{4\pi \varepsilon _{0}}}{\mathbf {r} _{01} \over {|\mathbf {r} _{01}|}^{3}}} where Note that ε 0 {\displaystyle \varepsilon _{0}} must be replaced with ε {\displaystyle \varepsilon } , permittivity , when charges are in non-empty media. When
3465-1026: A point charge, the resulting electric field, d E ( r ) {\displaystyle d\mathbf {E} (\mathbf {r} )} , at point r {\displaystyle \mathbf {r} } can be calculated as d E ( r ) = ρ ( r ′ ) 4 π ε 0 r ^ ′ | r ′ | 2 d v = ρ ( r ′ ) 4 π ε 0 r ′ | r ′ | 3 d v {\displaystyle d\mathbf {E} (\mathbf {r} )={\frac {\rho (\mathbf {r} ')}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}' \over {|\mathbf {r} '|}^{2}}dv={\frac {\rho (\mathbf {r} ')}{4\pi \varepsilon _{0}}}{\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}dv} where The total field
SECTION 20
#17328522456093630-1026: A point charge, the resulting electric field, d E ( r ) {\displaystyle d\mathbf {E} (\mathbf {r} )} , at point r {\displaystyle \mathbf {r} } can be calculated as d E ( r ) = ρ ( r ′ ) 4 π ε 0 r ^ ′ | r ′ | 2 d v = ρ ( r ′ ) 4 π ε 0 r ′ | r ′ | 3 d v {\displaystyle d\mathbf {E} (\mathbf {r} )={\frac {\rho (\mathbf {r} ')}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}' \over {|\mathbf {r} '|}^{2}}dv={\frac {\rho (\mathbf {r} ')}{4\pi \varepsilon _{0}}}{\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}dv} where The total field
3795-511: A posteriori, the previous form for E . The equations of electromagnetism are best described in a continuous description. However, charges are sometimes best described as discrete points; for example, some models may describe electrons as point sources where charge density is infinite on an infinitesimal section of space. A charge q {\displaystyle q} located at r 0 {\displaystyle \mathbf {r} _{0}} can be described mathematically as
3960-511: A posteriori, the previous form for E . The equations of electromagnetism are best described in a continuous description. However, charges are sometimes best described as discrete points; for example, some models may describe electrons as point sources where charge density is infinite on an infinitesimal section of space. A charge q {\displaystyle q} located at r 0 {\displaystyle \mathbf {r} _{0}} can be described mathematically as
4125-432: A rectangular void within this ordinary configuration, with current-contacts, as mentioned above, on the interior boundary of the void. (For simplicity, imagine the contacts on the boundary of the void lined up with the ordinary-configuration contacts on the exterior boundary.) In such a combined configuration, the two Hall effects may be realized and observed simultaneously in the same doubly connected device: A Hall effect on
4290-434: A representative concept; the field actually permeates all the intervening space between the lines. More or fewer lines may be drawn depending on the precision to which it is desired to represent the field. The study of electric fields created by stationary charges is called electrostatics . Faraday's law describes the relationship between a time-varying magnetic field and the electric field. One way of stating Faraday's law
4455-445: A result, the Hall effect is very useful as a means to measure either the carrier density or the magnetic field. One very important feature of the Hall effect is that it differentiates between positive charges moving in one direction and negative charges moving in the opposite. In the diagram above, the Hall effect with a negative charge carrier (the electron) is presented. But consider the same magnetic field and current are applied but
4620-548: A set of four coupled multi-dimensional partial differential equations which, when solved for a system, describe the combined behavior of the electromagnetic fields. In general, the force experienced by a test charge in an electromagnetic field is given by the Lorentz force law : F = q E + q v × B . {\displaystyle \mathbf {F} =q\mathbf {E} +q\mathbf {v} \times \mathbf {B} .} The total energy per unit volume stored by
4785-499: A set of four coupled multi-dimensional partial differential equations which, when solved for a system, describe the combined behavior of the electromagnetic fields. In general, the force experienced by a test charge in an electromagnetic field is given by the Lorentz force law : F = q E + q v × B . {\displaystyle \mathbf {F} =q\mathbf {E} +q\mathbf {v} \times \mathbf {B} .} The total energy per unit volume stored by
4950-441: A simpler treatment using electrostatics, time-varying magnetic fields are generally treated as a component of a unified electromagnetic field . The study of magnetic and electric fields that change over time is called electrodynamics . Electric fields are caused by electric charges , described by Gauss's law , and time varying magnetic fields , described by Faraday's law of induction . Together, these laws are enough to define
5115-417: A solution of: t a = t + | r − r s ( t a ) | c {\displaystyle t_{a}=\mathbf {t} +{\frac {|\mathbf {r} -\mathbf {r} _{s}(t_{a})|}{c}}} Since the physical interpretation of this indicates that the electric field at a point is governed by the particle's state at a point of time in
Hall effect - Misplaced Pages Continue
5280-417: A solution of: t a = t + | r − r s ( t a ) | c {\displaystyle t_{a}=\mathbf {t} +{\frac {|\mathbf {r} -\mathbf {r} _{s}(t_{a})|}{c}}} Since the physical interpretation of this indicates that the electric field at a point is governed by the particle's state at a point of time in
5445-488: A surface charge with surface charge density σ ( r ′ ) {\displaystyle \sigma (\mathbf {r} ')} on surface S {\displaystyle S} E ( r ) = 1 4 π ε 0 ∬ S σ ( r ′ ) r ′ | r ′ | 3 d
5610-488: A surface charge with surface charge density σ ( r ′ ) {\displaystyle \sigma (\mathbf {r} ')} on surface S {\displaystyle S} E ( r ) = 1 4 π ε 0 ∬ S σ ( r ′ ) r ′ | r ′ | 3 d
5775-400: A system is static, such that magnetic fields are not time-varying, then by Faraday's law, the electric field is curl-free . In this case, one can define an electric potential , that is, a function φ {\displaystyle \varphi } such that E = − ∇ φ {\displaystyle \mathbf {E} =-\nabla \varphi } . This
5940-400: A system is static, such that magnetic fields are not time-varying, then by Faraday's law, the electric field is curl-free . In this case, one can define an electric potential , that is, a function φ {\displaystyle \varphi } such that E = − ∇ φ {\displaystyle \mathbf {E} =-\nabla \varphi } . This
6105-553: A uniformly moving point charge is hence given by: E = q 4 π ε 0 r 3 1 − β 2 ( 1 − β 2 sin 2 θ ) 3 / 2 r , {\displaystyle \mathbf {E} ={\frac {q}{4\pi \varepsilon _{0}r^{3}}}{\frac {1-\beta ^{2}}{(1-\beta ^{2}\sin ^{2}\theta )^{3/2}}}\mathbf {r} ,} where q {\displaystyle q}
6270-553: A uniformly moving point charge is hence given by: E = q 4 π ε 0 r 3 1 − β 2 ( 1 − β 2 sin 2 θ ) 3 / 2 r , {\displaystyle \mathbf {E} ={\frac {q}{4\pi \varepsilon _{0}r^{3}}}{\frac {1-\beta ^{2}}{(1-\beta ^{2}\sin ^{2}\theta )^{3/2}}}\mathbf {r} ,} where q {\displaystyle q}
6435-975: Is a unit vector pointing from charged particle to the point in space, β s ( t ) {\textstyle {\boldsymbol {\beta }}_{s}(t)} is the velocity of the particle divided by the speed of light, and γ ( t ) {\textstyle \gamma (t)} is the corresponding Lorentz factor . The retarded time is given as solution of: t r = t − | r − r s ( t r ) | c {\displaystyle t_{r}=\mathbf {t} -{\frac {|\mathbf {r} -\mathbf {r} _{s}(t_{r})|}{c}}} The uniqueness of solution for t r {\textstyle {t_{r}}} for given t {\displaystyle \mathbf {t} } , r {\displaystyle \mathbf {r} } and r s ( t ) {\displaystyle r_{s}(t)}
6600-975: Is a unit vector pointing from charged particle to the point in space, β s ( t ) {\textstyle {\boldsymbol {\beta }}_{s}(t)} is the velocity of the particle divided by the speed of light, and γ ( t ) {\textstyle \gamma (t)} is the corresponding Lorentz factor . The retarded time is given as solution of: t r = t − | r − r s ( t r ) | c {\displaystyle t_{r}=\mathbf {t} -{\frac {|\mathbf {r} -\mathbf {r} _{s}(t_{r})|}{c}}} The uniqueness of solution for t r {\textstyle {t_{r}}} for given t {\displaystyle \mathbf {t} } , r {\displaystyle \mathbf {r} } and r s ( t ) {\displaystyle r_{s}(t)}
6765-929: Is analogous to the gravitational potential . The difference between the electric potential at two points in space is called the potential difference (or voltage) between the two points. In general, however, the electric field cannot be described independently of the magnetic field. Given the magnetic vector potential , A , defined so that B = ∇ × A {\displaystyle \mathbf {B} =\nabla \times \mathbf {A} } , one can still define an electric potential φ {\displaystyle \varphi } such that: E = − ∇ φ − ∂ A ∂ t , {\displaystyle \mathbf {E} =-\nabla \varphi -{\frac {\partial \mathbf {A} }{\partial t}},} where ∇ φ {\displaystyle \nabla \varphi }
Hall effect - Misplaced Pages Continue
6930-929: Is analogous to the gravitational potential . The difference between the electric potential at two points in space is called the potential difference (or voltage) between the two points. In general, however, the electric field cannot be described independently of the magnetic field. Given the magnetic vector potential , A , defined so that B = ∇ × A {\displaystyle \mathbf {B} =\nabla \times \mathbf {A} } , one can still define an electric potential φ {\displaystyle \varphi } such that: E = − ∇ φ − ∂ A ∂ t , {\displaystyle \mathbf {E} =-\nabla \varphi -{\frac {\partial \mathbf {A} }{\partial t}},} where ∇ φ {\displaystyle \nabla \varphi }
7095-593: Is assigned in the direction of the y -axis, (and not with the arrow of the induced electric field ξ y as in the image (pointing in the − y direction), which tells you where the field caused by the electrons is pointing). In wires, electrons instead of holes are flowing, so v x → − v x and q → − q . Also E y = − V H / w . Substituting these changes gives V H = v x B z w {\displaystyle V_{\mathrm {H} }=v_{x}B_{z}w} The conventional "hole" current
7260-419: Is contrarily more appropriate to think of the current as positive " holes " moving rather than negative electrons. A common source of confusion with the Hall effect in such materials is that holes moving one way are really electrons moving the opposite way, so one expects the Hall voltage polarity to be the same as if electrons were the charge carriers as in most metals and n-type semiconductors . Yet we observe
7425-423: Is defined at each point in space as the force that would be experienced by an infinitesimally small stationary test charge at that point divided by the charge. The electric field is defined in terms of force , and force is a vector (i.e. having both magnitude and direction ), so it follows that an electric field may be described by a vector field . The electric field acts between two charges similarly to
7590-829: Is described as a function of electric field, the equations of both fields are coupled and together form Maxwell's equations that describe both fields as a function of charges and currents . In the special case of a steady state (stationary charges and currents), the Maxwell-Faraday inductive effect disappears. The resulting two equations (Gauss's law ∇ ⋅ E = ρ ε 0 {\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}} and Faraday's law with no induction term ∇ × E = 0 {\displaystyle \nabla \times \mathbf {E} =0} ), taken together, are equivalent to Coulomb's law , which states that
7755-443: Is due to the nature of the current in a conductor. Current consists of the movement of many small charge carriers , typically electrons , holes , ions (see Electromigration ) or all three. When a magnetic field is present, these charges experience a force, called the Lorentz force . When such a magnetic field is absent, the charges follow approximately straight paths between collisions with impurities, phonons , etc. However, when
7920-481: Is equal to the negative time derivative of the magnetic field. In the absence of time-varying magnetic field, the electric field is therefore called conservative (i.e. curl-free). This implies there are two kinds of electric fields: electrostatic fields and fields arising from time-varying magnetic fields. While the curl-free nature of the static electric field allows for a simpler treatment using electrostatics, time-varying magnetic fields are generally treated as
8085-494: Is everywhere directed away from the charge if it is positive, and toward the charge if it is negative, and its magnitude decreases with the inverse square of the distance from the charge. The Coulomb force on a charge of magnitude q {\displaystyle q} at any point in space is equal to the product of the charge and the electric field at that point F = q E . {\displaystyle \mathbf {F} =q\mathbf {E} .} The SI unit of
8250-494: Is everywhere directed away from the charge if it is positive, and toward the charge if it is negative, and its magnitude decreases with the inverse square of the distance from the charge. The Coulomb force on a charge of magnitude q {\displaystyle q} at any point in space is equal to the product of the charge and the electric field at that point F = q E . {\displaystyle \mathbf {F} =q\mathbf {E} .} The SI unit of
8415-652: Is found by summing the contributions from all the increments of volume by integrating the charge density over the volume V {\displaystyle V} : E ( r ) = 1 4 π ε 0 ∭ V ρ ( r ′ ) r ′ | r ′ | 3 d v {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\iiint _{V}\,\rho (\mathbf {r} '){\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}dv} Similar equations follow for
SECTION 50
#17328522456098580-652: Is found by summing the contributions from all the increments of volume by integrating the charge density over the volume V {\displaystyle V} : E ( r ) = 1 4 π ε 0 ∭ V ρ ( r ′ ) r ′ | r ′ | 3 d v {\displaystyle \mathbf {E} (\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\iiint _{V}\,\rho (\mathbf {r} '){\mathbf {r} ' \over {|\mathbf {r} '|}^{3}}dv} Similar equations follow for
8745-545: Is frame-specific, and similarly for the associated energy. The total energy U EM stored in the electromagnetic field in a given volume V is U EM = 1 2 ∫ V ( ε | E | 2 + 1 μ | B | 2 ) d V . {\displaystyle U_{\text{EM}}={\frac {1}{2}}\int _{V}\left(\varepsilon |\mathbf {E} |^{2}+{\frac {1}{\mu }}|\mathbf {B} |^{2}\right)dV\,.} In
8910-545: Is frame-specific, and similarly for the associated energy. The total energy U EM stored in the electromagnetic field in a given volume V is U EM = 1 2 ∫ V ( ε | E | 2 + 1 μ | B | 2 ) d V . {\displaystyle U_{\text{EM}}={\frac {1}{2}}\int _{V}\left(\varepsilon |\mathbf {E} |^{2}+{\frac {1}{\mu }}|\mathbf {B} |^{2}\right)dV\,.} In
9075-556: Is in the negative direction of the electron current and the negative of the electrical charge which gives I x = ntw (− v x )(− e ) where n is charge carrier density , tw is the cross-sectional area, and − e is the charge of each electron. Solving for w {\displaystyle w} and plugging into the above gives the Hall voltage: V H = I x B z n t e {\displaystyle V_{\mathrm {H} }={\frac {I_{x}B_{z}}{nte}}} If
9240-426: Is in the order of 10 V⋅m , achieved by applying a voltage of the order of 1 volt between conductors spaced 1 μm apart. Electromagnetic fields are electric and magnetic fields, which may change with time, for instance when charges are in motion. Moving charges produce a magnetic field in accordance with Ampère's circuital law ( with Maxwell's addition ), which, along with Maxwell's other equations, defines
9405-426: Is in the order of 10 V⋅m , achieved by applying a voltage of the order of 1 volt between conductors spaced 1 μm apart. Electromagnetic fields are electric and magnetic fields, which may change with time, for instance when charges are in motion. Moving charges produce a magnetic field in accordance with Ampère's circuital law ( with Maxwell's addition ), which, along with Maxwell's other equations, defines
9570-401: Is injected via contacts that lie on the boundary or edge of the void. The charge then flows outside the void, within the metal or semiconductor material. The effect becomes observable, in a perpendicular applied magnetic field, as a Hall voltage appearing on either side of a line connecting the current-contacts. It exhibits apparent sign reversal in comparison to the "ordinary" effect occurring in
9735-413: Is kept in a magnetic field, the charge carriers of the semiconductor experience a force in a direction perpendicular to both the magnetic field and the current. At equilibrium, a voltage appears at the semiconductor edges. The simple formula for the Hall coefficient given above is usually a good explanation when conduction is dominated by a single charge carrier . However, in semiconductors and many metals
9900-477: Is not as clear as E (effectively the field applied to the material) or P (induced field due to the dipoles in the material), but still serves as a convenient mathematical simplification, since Maxwell's equations can be simplified in terms of free charges and currents . The E and D fields are related by the permittivity of the material, ε . For linear, homogeneous , isotropic materials E and D are proportional and constant throughout
10065-477: Is not as clear as E (effectively the field applied to the material) or P (induced field due to the dipoles in the material), but still serves as a convenient mathematical simplification, since Maxwell's equations can be simplified in terms of free charges and currents . The E and D fields are related by the permittivity of the material, ε . For linear, homogeneous , isotropic materials E and D are proportional and constant throughout
SECTION 60
#173285224560910230-415: Is one of the four fundamental interactions of nature. Electric fields are important in many areas of physics , and are exploited in electrical technology. For example, in atomic physics and chemistry , the interaction in the electric field between the atomic nucleus and electrons is the force that holds these particles together in atoms. Similarly, the interaction in the electric field between atoms
10395-1821: Is possible in a systems of charges. For arbitrarily moving point charges, propagation of potential fields such as Lorenz gauge fields at the speed of light needs to be accounted for by using Liénard–Wiechert potential . Since the potentials satisfy Maxwell's equations , the fields derived for point charge also satisfy Maxwell's equations . The electric field is expressed as: E ( r , t ) = 1 4 π ε 0 ( q ( n s − β s ) γ 2 ( 1 − n s ⋅ β s ) 3 | r − r s | 2 + q n s × ( ( n s − β s ) × β s ˙ ) c ( 1 − n s ⋅ β s ) 3 | r − r s | ) t = t r {\displaystyle \mathbf {E} (\mathbf {r} ,\mathbf {t} )={\frac {1}{4\pi \varepsilon _{0}}}\left({\frac {q(\mathbf {n} _{s}-{\boldsymbol {\beta }}_{s})}{\gamma ^{2}(1-\mathbf {n} _{s}\cdot {\boldsymbol {\beta }}_{s})^{3}|\mathbf {r} -\mathbf {r} _{s}|^{2}}}+{\frac {q\mathbf {n} _{s}\times {\big (}(\mathbf {n} _{s}-{\boldsymbol {\beta }}_{s})\times {\dot {{\boldsymbol {\beta }}_{s}}}{\big )}}{c(1-\mathbf {n} _{s}\cdot {\boldsymbol {\beta }}_{s})^{3}|\mathbf {r} -\mathbf {r} _{s}|}}\right)_{t=t_{r}}} where q {\displaystyle q}
10560-1821: Is possible in a systems of charges. For arbitrarily moving point charges, propagation of potential fields such as Lorenz gauge fields at the speed of light needs to be accounted for by using Liénard–Wiechert potential . Since the potentials satisfy Maxwell's equations , the fields derived for point charge also satisfy Maxwell's equations . The electric field is expressed as: E ( r , t ) = 1 4 π ε 0 ( q ( n s − β s ) γ 2 ( 1 − n s ⋅ β s ) 3 | r − r s | 2 + q n s × ( ( n s − β s ) × β s ˙ ) c ( 1 − n s ⋅ β s ) 3 | r − r s | ) t = t r {\displaystyle \mathbf {E} (\mathbf {r} ,\mathbf {t} )={\frac {1}{4\pi \varepsilon _{0}}}\left({\frac {q(\mathbf {n} _{s}-{\boldsymbol {\beta }}_{s})}{\gamma ^{2}(1-\mathbf {n} _{s}\cdot {\boldsymbol {\beta }}_{s})^{3}|\mathbf {r} -\mathbf {r} _{s}|^{2}}}+{\frac {q\mathbf {n} _{s}\times {\big (}(\mathbf {n} _{s}-{\boldsymbol {\beta }}_{s})\times {\dot {{\boldsymbol {\beta }}_{s}}}{\big )}}{c(1-\mathbf {n} _{s}\cdot {\boldsymbol {\beta }}_{s})^{3}|\mathbf {r} -\mathbf {r} _{s}|}}\right)_{t=t_{r}}} where q {\displaystyle q}
10725-550: Is similar to Newton's law of universal gravitation : F = m ( − G M r ^ | r | 2 ) = m g {\displaystyle \mathbf {F} =m\left(-GM{\frac {\mathbf {\hat {r}} }{|\mathbf {r} |^{2}}}\right)=m\mathbf {g} } (where r ^ = r | r | {\textstyle \mathbf {\hat {r}} =\mathbf {\frac {r}{|r|}} } ). This suggests similarities between
10890-550: Is similar to Newton's law of universal gravitation : F = m ( − G M r ^ | r | 2 ) = m g {\displaystyle \mathbf {F} =m\left(-GM{\frac {\mathbf {\hat {r}} }{|\mathbf {r} |^{2}}}\right)=m\mathbf {g} } (where r ^ = r | r | {\textstyle \mathbf {\hat {r}} =\mathbf {\frac {r}{|r|}} } ). This suggests similarities between
11055-426: Is that the curl of the electric field is equal to the negative time derivative of the magnetic field. In the absence of time-varying magnetic field, the electric field is therefore called conservative (i.e. curl-free). This implies there are two kinds of electric fields: electrostatic fields and fields arising from time-varying magnetic fields. While the curl-free nature of the static electric field allows for
11220-518: Is the current density of the carrier electrons, and E y is the induced electric field. In SI units, this becomes R H = E y j x B = V H t I B = 1 n e . {\displaystyle R_{\mathrm {H} }={\frac {E_{y}}{j_{x}B}}={\frac {V_{\mathrm {H} }t}{IB}}={\frac {1}{ne}}.} (The units of R H are usually expressed as m/C, or Ω·cm/ G , or other variants.) As
11385-415: Is the current density , μ 0 {\displaystyle \mu _{0}} is the vacuum permeability , and ε 0 {\displaystyle \varepsilon _{0}} is the vacuum permittivity . Both the electric current density and the partial derivative of the electric field with respect to time, contribute to the curl of the magnetic field. In addition,
11550-415: Is the current density , μ 0 {\displaystyle \mu _{0}} is the vacuum permeability , and ε 0 {\displaystyle \varepsilon _{0}} is the vacuum permittivity . Both the electric current density and the partial derivative of the electric field with respect to time, contribute to the curl of the magnetic field. In addition,
11715-490: Is the electric field at point r 0 {\displaystyle \mathbf {r} _{0}} due to the point charge q 1 {\displaystyle q_{1}} ; it is a vector-valued function equal to the Coulomb force per unit charge that a positive point charge would experience at the position r 0 {\displaystyle \mathbf {r} _{0}} . Since this formula gives
11880-440: Is the electric field at point r 0 {\displaystyle \mathbf {r} _{0}} due to the point charge q 1 {\displaystyle q_{1}} ; it is a vector-valued function equal to the Coulomb force per unit charge that a positive point charge would experience at the position r 0 {\displaystyle \mathbf {r} _{0}} . Since this formula gives
12045-746: Is the gradient of the electric potential and ∂ A ∂ t {\displaystyle {\frac {\partial \mathbf {A} }{\partial t}}} is the partial derivative of A with respect to time. Faraday's law of induction can be recovered by taking the curl of that equation ∇ × E = − ∂ ( ∇ × A ) ∂ t = − ∂ B ∂ t , {\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial (\nabla \times \mathbf {A} )}{\partial t}}=-{\frac {\partial \mathbf {B} }{\partial t}},} which justifies,
12210-746: Is the gradient of the electric potential and ∂ A ∂ t {\displaystyle {\frac {\partial \mathbf {A} }{\partial t}}} is the partial derivative of A with respect to time. Faraday's law of induction can be recovered by taking the curl of that equation ∇ × E = − ∂ ( ∇ × A ) ∂ t = − ∂ B ∂ t , {\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial (\nabla \times \mathbf {A} )}{\partial t}}=-{\frac {\partial \mathbf {B} }{\partial t}},} which justifies,
12375-516: Is the physical field that surrounds electrically charged particles . Charged particles exert attractive forces on each other when their charges are opposite, and repulse each other when their charges are the same. Because these forces are exerted mutually, two charges must be present for the forces to take place. The electric field of a single charge (or group of charges) describes their capacity to exert such forces on another charged object. These forces are described by Coulomb's law , which says that
12540-418: Is the potential difference between the plates and d is the distance separating the plates. The negative sign arises as positive charges repel, so a positive charge will experience a force away from the positively charged plate, in the opposite direction to that in which the voltage increases. In micro- and nano-applications, for instance in relation to semiconductors, a typical magnitude of an electric field
12705-418: Is the potential difference between the plates and d is the distance separating the plates. The negative sign arises as positive charges repel, so a positive charge will experience a force away from the positively charged plate, in the opposite direction to that in which the voltage increases. In micro- and nano-applications, for instance in relation to semiconductors, a typical magnitude of an electric field
12870-427: Is the charge of the point source, t r {\textstyle {t_{r}}} is retarded time or the time at which the source's contribution of the electric field originated, r s ( t ) {\textstyle {r}_{s}(t)} is the position vector of the particle, n s ( r , t ) {\textstyle {n}_{s}(\mathbf {r} ,t)}
13035-427: Is the charge of the point source, t r {\textstyle {t_{r}}} is retarded time or the time at which the source's contribution of the electric field originated, r s ( t ) {\textstyle {r}_{s}(t)} is the position vector of the particle, n s ( r , t ) {\textstyle {n}_{s}(\mathbf {r} ,t)}
13200-448: Is the charge of the point source, r {\displaystyle \mathbf {r} } is the position vector from the point source to the point in space, β {\displaystyle \beta } is the ratio of observed speed of the charge particle to the speed of light and θ {\displaystyle \theta } is the angle between r {\displaystyle \mathbf {r} } and
13365-448: Is the charge of the point source, r {\displaystyle \mathbf {r} } is the position vector from the point source to the point in space, β {\displaystyle \beta } is the ratio of observed speed of the charge particle to the speed of light and θ {\displaystyle \theta } is the angle between r {\displaystyle \mathbf {r} } and
13530-415: Is the electron concentration, p the hole concentration, μ e the electron mobility, μ h the hole mobility and e the elementary charge. For large applied fields the simpler expression analogous to that for a single carrier type holds. Although it is well known that magnetic fields play an important role in star formation, research models indicate that Hall diffusion critically influences
13695-409: Is the force responsible for chemical bonding that result in molecules . The electric field is defined as a vector field that associates to each point in space the force per unit of charge exerted on an infinitesimal test charge at rest at that point. The SI unit for the electric field is the volt per meter (V/m), which is equal to the newton per coulomb (N/C). The electric field
13860-453: Is the same—an electron moving up is the same current as a positive charge moving down. And with the fingers (magnetic field) also being the same, interestingly the charge carrier gets deflected to the left in the diagram regardless of whether it is positive or negative. But if positive carriers are deflected to the left, they would build a relatively positive voltage on the left whereas if negative carriers (namely electrons) are, they build up
14025-465: Is the spin current generated by the applied current density j e {\displaystyle j_{e}} . For mercury telluride two dimensional quantum wells with strong spin-orbit coupling, in zero magnetic field, at low temperature, the quantum spin Hall effect has been observed in 2007. In ferromagnetic materials (and paramagnetic materials in a magnetic field ), the Hall resistivity includes an additional contribution, known as
14190-446: Is uniform linear charge density. where σ {\displaystyle \sigma } is uniform surface charge density. where λ {\displaystyle \lambda } is uniform linear charge density. outside the sphere, where Q {\displaystyle Q} is the total charge uniformly distributed in the volume. Electric field An electric field (sometimes called E-field )
14355-455: Is useful in calculating the field created by multiple point charges. If charges q 1 , q 2 , … , q n {\displaystyle q_{1},q_{2},\dots ,q_{n}} are stationary in space at points r 1 , r 2 , … , r n {\displaystyle \mathbf {r} _{1},\mathbf {r} _{2},\dots ,\mathbf {r} _{n}} , in
14520-455: Is useful in calculating the field created by multiple point charges. If charges q 1 , q 2 , … , q n {\displaystyle q_{1},q_{2},\dots ,q_{n}} are stationary in space at points r 1 , r 2 , … , r n {\displaystyle \mathbf {r} _{1},\mathbf {r} _{2},\dots ,\mathbf {r} _{n}} , in
14685-472: Is valid for charged particles moving slower than speed of light. Electromagnetic radiation of accelerating charges is known to be caused by the acceleration dependent term in the electric field from which relativistic correction for Larmor formula is obtained. There exist yet another set of solutions for Maxwell's equation of the same form but for advanced time t a {\textstyle {t_{a}}} instead of retarded time given as
14850-472: Is valid for charged particles moving slower than speed of light. Electromagnetic radiation of accelerating charges is known to be caused by the acceleration dependent term in the electric field from which relativistic correction for Larmor formula is obtained. There exist yet another set of solutions for Maxwell's equation of the same form but for advanced time t a {\textstyle {t_{a}}} instead of retarded time given as
15015-453: The E and D fields are not parallel, and so E and D are related by the permittivity tensor (a 2nd order tensor field ), in component form: D i = ε i j E j {\displaystyle D_{i}=\varepsilon _{ij}E_{j}} For non-linear media, E and D are not proportional. Materials can have varying extents of linearity, homogeneity and isotropy. The invariance of
15180-453: The E and D fields are not parallel, and so E and D are related by the permittivity tensor (a 2nd order tensor field ), in component form: D i = ε i j E j {\displaystyle D_{i}=\varepsilon _{ij}E_{j}} For non-linear media, E and D are not proportional. Materials can have varying extents of linearity, homogeneity and isotropy. The invariance of
15345-494: The Hall angle , θ , which also gives the Hall parameter: β = tan ( θ ) . {\displaystyle \beta =\tan(\theta ).} The Hall Effects family has expanded to encompass other quasi-particles in semiconductor nanostructures. Specifically, a set of Hall Effects has emerged based on excitons and exciton-polaritons n 2D materials and quantum wells. Hall sensors amplify and use
15510-505: The Maxwell–Faraday equation states ∇ × E = − ∂ B ∂ t . {\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}.} These represent two of Maxwell's four equations and they intricately link the electric and magnetic fields together, resulting in the electromagnetic field . The equations represent
15675-448: The Maxwell–Faraday equation states ∇ × E = − ∂ B ∂ t . {\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}.} These represent two of Maxwell's four equations and they intricately link the electric and magnetic fields together, resulting in the electromagnetic field . The equations represent
15840-416: The anomalous Hall effect (or the extraordinary Hall effect ), which depends directly on the magnetization of the material, and is often much larger than the ordinary Hall effect. (Note that this effect is not due to the contribution of the magnetization to the total magnetic field .) For example, in nickel, the anomalous Hall coefficient is about 100 times larger than the ordinary Hall coefficient near
16005-517: The electromagnetic field is u EM = ε 2 | E | 2 + 1 2 μ | B | 2 {\displaystyle u_{\text{EM}}={\frac {\varepsilon }{2}}|\mathbf {E} |^{2}+{\frac {1}{2\mu }}|\mathbf {B} |^{2}} where ε is the permittivity of the medium in which the field exists, μ {\displaystyle \mu } its magnetic permeability , and E and B are
16170-517: The electromagnetic field is u EM = ε 2 | E | 2 + 1 2 μ | B | 2 {\displaystyle u_{\text{EM}}={\frac {\varepsilon }{2}}|\mathbf {E} |^{2}+{\frac {1}{2\mu }}|\mathbf {B} |^{2}} where ε is the permittivity of the medium in which the field exists, μ {\displaystyle \mu } its magnetic permeability , and E and B are
16335-409: The electromagnetic field , Electromagnetism is one of the four fundamental interactions of nature. Electric fields are important in many areas of physics , and are exploited in electrical technology. For example, in atomic physics and chemistry , the interaction in the electric field between the atomic nucleus and electrons is the force that holds these particles together in atoms. Similarly,
16500-474: The electron was discovered, his measurements of the tiny effect produced in the apparatus he used were an experimental tour de force , published under the name "On a New Action of the Magnet on Electric Currents". The term ordinary Hall effect can be used to distinguish the effect described in the introduction from a related effect which occurs across a void or hole in a semiconductor or metal plate when current
16665-402: The newton per coulomb (N/C). The electric field is defined at each point in space as the force that would be experienced by an infinitesimally small stationary test charge at that point divided by the charge. The electric field is defined in terms of force , and force is a vector (i.e. having both magnitude and direction ), so it follows that an electric field may be described by
16830-419: The speed of light . Advanced time, which also provides a solution for Maxwell's law are ignored as an unphysical solution. For the motion of a charged particle , considering for example the case of a moving particle with the above described electric field coming to an abrupt stop, the electric fields at points far from it do not immediately revert to that classically given for a stationary charge. On stopping,
16995-419: The speed of light . Advanced time, which also provides a solution for Maxwell's law are ignored as an unphysical solution. For the motion of a charged particle , considering for example the case of a moving particle with the above described electric field coming to an abrupt stop, the electric fields at points far from it do not immediately revert to that classically given for a stationary charge. On stopping,
17160-417: The strength of the field is proportional to the density of the lines. Field lines due to stationary charges have several important properties, including that they always originate from positive charges and terminate at negative charges, they enter all good conductors at right angles, and they never cross or close in on themselves. The field lines are a representative concept; the field actually permeates all
17325-504: The Curie temperature, but the two are similar at very low temperatures. Although a well-recognized phenomenon, there is still debate about its origins in the various materials. The anomalous Hall effect can be either an extrinsic (disorder-related) effect due to spin -dependent scattering of the charge carriers , or an intrinsic effect which can be described in terms of the Berry phase effect in
17490-404: The Hall effect for a variety of sensing applications. The Corbino effect, named after its discoverer Orso Mario Corbino , is a phenomenon involving the Hall effect, but a disc-shaped metal sample is used in place of a rectangular one. Because of its shape the Corbino disc allows the observation of Hall effect–based magnetoresistance without the associated Hall voltage. A radial current through
17655-1272: The absence of currents, the superposition principle says that the resulting field is the sum of fields generated by each particle as described by Coulomb's law: E ( r ) = E 1 ( r ) + E 2 ( r ) + ⋯ + E n ( r ) = 1 4 π ε 0 ∑ i = 1 n q i r ^ i | r i | 2 = 1 4 π ε 0 ∑ i = 1 n q i r i | r i | 3 {\displaystyle {\begin{aligned}\mathbf {E} (\mathbf {r} )=\mathbf {E} _{1}(\mathbf {r} )+\mathbf {E} _{2}(\mathbf {r} )+\dots +\mathbf {E} _{n}(\mathbf {r} )={1 \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{{\hat {\mathbf {r} }}_{i} \over {|\mathbf {r} _{i}|}^{2}}={1 \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{\mathbf {r} _{i} \over {|\mathbf {r} _{i}|}^{3}}\end{aligned}}} where The superposition principle allows for
17820-1272: The absence of currents, the superposition principle says that the resulting field is the sum of fields generated by each particle as described by Coulomb's law: E ( r ) = E 1 ( r ) + E 2 ( r ) + ⋯ + E n ( r ) = 1 4 π ε 0 ∑ i = 1 n q i r ^ i | r i | 2 = 1 4 π ε 0 ∑ i = 1 n q i r i | r i | 3 {\displaystyle {\begin{aligned}\mathbf {E} (\mathbf {r} )=\mathbf {E} _{1}(\mathbf {r} )+\mathbf {E} _{2}(\mathbf {r} )+\dots +\mathbf {E} _{n}(\mathbf {r} )={1 \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{{\hat {\mathbf {r} }}_{i} \over {|\mathbf {r} _{i}|}^{2}}={1 \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{\mathbf {r} _{i} \over {|\mathbf {r} _{i}|}^{3}}\end{aligned}}} where The superposition principle allows for
17985-841: The behavior of the electric field. However, since the magnetic field is described as a function of electric field, the equations of both fields are coupled and together form Maxwell's equations that describe both fields as a function of charges and currents . In the special case of a steady state (stationary charges and currents), the Maxwell-Faraday inductive effect disappears. The resulting two equations (Gauss's law ∇ ⋅ E = ρ ε 0 {\displaystyle \nabla \cdot \mathbf {E} ={\frac {\rho }{\varepsilon _{0}}}} and Faraday's law with no induction term ∇ × E = 0 {\displaystyle \nabla \times \mathbf {E} =0} ), taken together, are equivalent to Coulomb's law , which states that
18150-489: The calculation of the electric field due to a distribution of charge density ρ ( r ) {\displaystyle \rho (\mathbf {r} )} . By considering the charge ρ ( r ′ ) d v {\displaystyle \rho (\mathbf {r} ')dv} in each small volume of space d v {\displaystyle dv} at point r ′ {\displaystyle \mathbf {r} '} as
18315-489: The calculation of the electric field due to a distribution of charge density ρ ( r ) {\displaystyle \rho (\mathbf {r} )} . By considering the charge ρ ( r ′ ) d v {\displaystyle \rho (\mathbf {r} ')dv} in each small volume of space d v {\displaystyle dv} at point r ′ {\displaystyle \mathbf {r} '} as
18480-645: The charge build up had been positive (as it appears in some metals and semiconductors), then the V H assigned in the image would have been negative (positive charge would have built up on the left side). The Hall coefficient is defined as R H = E y j x B z {\displaystyle R_{\mathrm {H} }={\frac {E_{y}}{j_{x}B_{z}}}} or E = − R H ( J c × B ) {\displaystyle \mathbf {E} =-R_{\mathrm {H} }(\mathbf {J} _{c}\times \mathbf {B} )} where j
18645-698: The charges q 0 {\displaystyle q_{0}} and q 1 {\displaystyle q_{1}} have the same sign this force is positive, directed away from the other charge, indicating the particles repel each other. When the charges have unlike signs the force is negative, indicating the particles attract. To make it easy to calculate the Coulomb force on any charge at position r 0 {\displaystyle \mathbf {r} _{0}} this expression can be divided by q 0 {\displaystyle q_{0}} leaving an expression that only depends on
18810-649: The charges q 0 {\displaystyle q_{0}} and q 1 {\displaystyle q_{1}} have the same sign this force is positive, directed away from the other charge, indicating the particles repel each other. When the charges have unlike signs the force is negative, indicating the particles attract. To make it easy to calculate the Coulomb force on any charge at position r 0 {\displaystyle \mathbf {r} _{0}} this expression can be divided by q 0 {\displaystyle q_{0}} leaving an expression that only depends on
18975-721: The crystal momentum space ( k -space). The Hall effect in an ionized gas ( plasma ) is significantly different from the Hall effect in solids (where the Hall parameter is always much less than unity). In a plasma, the Hall parameter can take any value. The Hall parameter, β , in a plasma is the ratio between the electron gyrofrequency , Ω e , and the electron-heavy particle collision frequency, ν : β = Ω e ν = e B m e ν {\displaystyle \beta ={\frac {\Omega _{\mathrm {e} }}{\nu }}={\frac {eB}{m_{\mathrm {e} }\nu }}} where The Hall parameter value increases with
19140-444: The current and magnetic field. In the 1820s, André-Marie Ampère observed this underlying mechanism that led to the discovery of the Hall effect. However it was not until a solid mathematical basis for electromagnetism was systematized by James Clerk Maxwell 's " On Physical Lines of Force " (published in 1861–1862) that details of the interaction between magnets and electric current could be understood. Edwin Hall then explored
19305-430: The current is carried inside the Hall effect device by a positive particle. The particle would of course have to be moving in the opposite direction of the electron in order for the current to be the same—down in the diagram, not up like the electron is. And thus, mnemonically speaking, your thumb in the Lorentz force law , representing (conventional) current, would be pointing the same direction as before, because current
19470-406: The direction of the voltage is opposite to the derivation below. For a simple metal where there is only one type of charge carrier (electrons), the Hall voltage V H can be derived by using the Lorentz force and seeing that, in the steady-state condition, charges are not moving in the y -axis direction. Thus, the magnetic force on each electron in the y -axis direction is cancelled by
19635-419: The dynamics of gravitational collapse that forms protostars. For a two-dimensional electron system which can be produced in a MOSFET , in the presence of large magnetic field strength and low temperature , one can observe the quantum Hall effect, in which the Hall conductance σ undergoes quantum Hall transitions to take on the quantized values. The spin Hall effect consists in the spin accumulation on
19800-427: The electric and magnetic field vectors. As E and B fields are coupled, it would be misleading to split this expression into "electric" and "magnetic" contributions. In particular, an electrostatic field in any given frame of reference in general transforms into a field with a magnetic component in a relatively moving frame. Accordingly, decomposing the electromagnetic field into an electric and magnetic component
19965-427: The electric and magnetic field vectors. As E and B fields are coupled, it would be misleading to split this expression into "electric" and "magnetic" contributions. In particular, an electrostatic field in any given frame of reference in general transforms into a field with a magnetic component in a relatively moving frame. Accordingly, decomposing the electromagnetic field into an electric and magnetic component
20130-429: The electric field E and the gravitational field g , or their associated potentials. Mass is sometimes called "gravitational charge". Electrostatic and gravitational forces both are central , conservative and obey an inverse-square law . A uniform field is one in which the electric field is constant at every point. It can be approximated by placing two conducting plates parallel to each other and maintaining
20295-429: The electric field E and the gravitational field g , or their associated potentials. Mass is sometimes called "gravitational charge". Electrostatic and gravitational forces both are central , conservative and obey an inverse-square law . A uniform field is one in which the electric field is constant at every point. It can be approximated by placing two conducting plates parallel to each other and maintaining
20460-482: The electric field is the newton per coulomb (N/C), or volt per meter (V/m); in terms of the SI base units it is kg⋅m⋅s ⋅A . Due to the linearity of Maxwell's equations , electric fields satisfy the superposition principle , which states that the total electric field, at a point, due to a collection of charges is equal to the vector sum of the electric fields at that point due to the individual charges. This principle
20625-438: The electric field is the newton per coulomb (N/C), or volt per meter (V/m); in terms of the SI base units it is kg⋅m⋅s ⋅A . Due to the linearity of Maxwell's equations , electric fields satisfy the superposition principle , which states that the total electric field, at a point, due to a collection of charges is equal to the vector sum of the electric fields at that point due to the individual charges. This principle
20790-407: The electric field magnitude and direction at any point r 0 {\displaystyle \mathbf {r} _{0}} in space (except at the location of the charge itself, r 1 {\displaystyle \mathbf {r} _{1}} , where it becomes infinite) it defines a vector field . From the above formula it can be seen that the electric field due to a point charge
20955-407: The electric field magnitude and direction at any point r 0 {\displaystyle \mathbf {r} _{0}} in space (except at the location of the charge itself, r 1 {\displaystyle \mathbf {r} _{1}} , where it becomes infinite) it defines a vector field . From the above formula it can be seen that the electric field due to a point charge
21120-529: The external boundary that is proportional to the current injected only via the outer boundary, and an apparently sign-reversed Hall effect on the interior boundary that is proportional to the current injected only via the interior boundary. The superposition of multiple Hall effects may be realized by placing multiple voids within the Hall element, with current and voltage contacts on the boundary of each void. Further "Hall effects" may have additional physical mechanisms but are built on these basics. The Hall effect
21285-488: The field around the stationary points begin to revert to the expected state and this effect propagates outwards at the speed of light while the electric field lines far away from this will continue to point radially towards an assumed moving charge. This virtual particle will never be outside the range of propagation of the disturbance in electromagnetic field , since charged particles are restricted to have speeds slower than that of light, which makes it impossible to construct
21450-488: The field around the stationary points begin to revert to the expected state and this effect propagates outwards at the speed of light while the electric field lines far away from this will continue to point radially towards an assumed moving charge. This virtual particle will never be outside the range of propagation of the disturbance in electromagnetic field , since charged particles are restricted to have speeds slower than that of light, which makes it impossible to construct
21615-435: The field. Coulomb's law, which describes the interaction of electric charges: F = q ( Q 4 π ε 0 r ^ | r | 2 ) = q E {\displaystyle \mathbf {F} =q\left({\frac {Q}{4\pi \varepsilon _{0}}}{\frac {\mathbf {\hat {r}} }{|\mathbf {r} |^{2}}}\right)=q\mathbf {E} }
21780-435: The field. Coulomb's law, which describes the interaction of electric charges: F = q ( Q 4 π ε 0 r ^ | r | 2 ) = q E {\displaystyle \mathbf {F} =q\left({\frac {Q}{4\pi \varepsilon _{0}}}{\frac {\mathbf {\hat {r}} }{|\mathbf {r} |^{2}}}\right)=q\mathbf {E} }
21945-400: The form of Maxwell's equations under Lorentz transformation can be used to derive the electric field of a uniformly moving point charge. The charge of a particle is considered frame invariant, as supported by experimental evidence. Alternatively the electric field of uniformly moving point charges can be derived from the Lorentz transformation of four-force experienced by test charges in
22110-400: The form of Maxwell's equations under Lorentz transformation can be used to derive the electric field of a uniformly moving point charge. The charge of a particle is considered frame invariant, as supported by experimental evidence. Alternatively the electric field of uniformly moving point charges can be derived from the Lorentz transformation of four-force experienced by test charges in
22275-452: The future, it is considered as an unphysical solution and hence neglected. However, there have been theories exploring the advanced time solutions of Maxwell's equations , such as Feynman Wheeler absorber theory . The above equation, although consistent with that of uniformly moving point charges as well as its non-relativistic limit, are not corrected for quantum-mechanical effects. where λ {\displaystyle \lambda }
22440-452: The future, it is considered as an unphysical solution and hence neglected. However, there have been theories exploring the advanced time solutions of Maxwell's equations , such as Feynman Wheeler absorber theory . The above equation, although consistent with that of uniformly moving point charges as well as its non-relativistic limit, are not corrected for quantum-mechanical effects. where λ {\displaystyle \lambda }
22605-475: The greater the magnitude of the charges, the greater the force, and the greater the distance between them, the weaker the force. Thus, we may informally say that the greater the charge of an object, the stronger its electric field. Similarly, an electric field is stronger nearer charged objects and weaker further away. Electric fields originate from electric charges and time-varying electric currents . Electric fields and magnetic fields are both manifestations of
22770-405: The interaction in the electric field between atoms is the force responsible for chemical bonding that result in molecules . The electric field is defined as a vector field that associates to each point in space the force per unit of charge exerted on an infinitesimal test charge at rest at that point. The SI unit for the electric field is the volt per meter (V/m), which is equal to
22935-416: The intervening space between the lines. More or fewer lines may be drawn depending on the precision to which it is desired to represent the field. The study of electric fields created by stationary charges is called electrostatics . Faraday's law describes the relationship between a time-varying magnetic field and the electric field. One way of stating Faraday's law is that the curl of the electric field
23100-773: The lateral boundaries of a current-carrying sample. No magnetic field is needed. It was predicted by Mikhail Dyakonov and V. I. Perel in 1971 and observed experimentally more than 30 years later, both in semiconductors and in metals, at cryogenic as well as at room temperatures. The quantity describing the strength of the Spin Hall effect is known as Spin Hall angle, and it is defined as: θ S H = 2 e ℏ | j s | | j e | {\displaystyle \theta _{SH}={\frac {2e}{\hbar }}{\frac {|j_{s}|}{|j_{e}|}}} Where j s {\displaystyle j_{s}}
23265-464: The magnetic field strength. Physically, the trajectories of electrons are curved by the Lorentz force . Nevertheless, when the Hall parameter is low, their motion between two encounters with heavy particles ( neutral or ion ) is almost linear. But if the Hall parameter is high, the electron movements are highly curved. The current density vector, J , is no longer collinear with the electric field vector, E . The two vectors J and E make
23430-507: The magnetic field, B {\displaystyle \mathbf {B} } , in terms of its curl: ∇ × B = μ 0 ( J + ε 0 ∂ E ∂ t ) , {\displaystyle \nabla \times \mathbf {B} =\mu _{0}\left(\mathbf {J} +\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right),} where J {\displaystyle \mathbf {J} }
23595-507: The magnetic field, B {\displaystyle \mathbf {B} } , in terms of its curl: ∇ × B = μ 0 ( J + ε 0 ∂ E ∂ t ) , {\displaystyle \nabla \times \mathbf {B} =\mu _{0}\left(\mathbf {J} +\varepsilon _{0}{\frac {\partial \mathbf {E} }{\partial t}}\right),} where J {\displaystyle \mathbf {J} }
23760-404: The modern quantum mechanical theory of quasiparticles wherein the collective quantized motion of multiple particles can, in a real physical sense, be considered to be a particle in its own right (albeit not an elementary one). Unrelatedly, inhomogeneity in the conductive sample can result in a spurious sign of the Hall effect, even in ideal van der Pauw configuration of electrodes. For example,
23925-449: The observed velocity of the charged particle. The above equation reduces to that given by Coulomb's law for non-relativistic speeds of the point charge. Spherical symmetry is not satisfied due to breaking of symmetry in the problem by specification of direction of velocity for calculation of field. To illustrate this, field lines of moving charges are sometimes represented as unequally spaced radial lines which would appear equally spaced in
24090-449: The observed velocity of the charged particle. The above equation reduces to that given by Coulomb's law for non-relativistic speeds of the point charge. Spherical symmetry is not satisfied due to breaking of symmetry in the problem by specification of direction of velocity for calculation of field. To illustrate this, field lines of moving charges are sometimes represented as unequally spaced radial lines which would appear equally spaced in
24255-458: The opposite polarity of Hall voltage, indicating positive charge carriers. However, of course there are no actual positrons or other positive elementary particles carrying the charge in p-type semiconductors , hence the name "holes". In the same way as the oversimplistic picture of light in glass as photons being absorbed and re-emitted to explain refraction breaks down upon closer scrutiny, this apparent contradiction too can only be resolved by
24420-820: The other charge (the source charge) E 1 ( r 0 ) = F 01 q 0 = q 1 4 π ε 0 r ^ 01 | r 01 | 2 = q 1 4 π ε 0 r 01 | r 01 | 3 {\displaystyle \mathbf {E} _{1}(\mathbf {r} _{0})={\frac {\mathbf {F} _{01}}{q_{0}}}={\frac {q_{1}}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}_{01} \over {|\mathbf {r} _{01}|}^{2}}={\frac {q_{1}}{4\pi \varepsilon _{0}}}{\mathbf {r} _{01} \over {|\mathbf {r} _{01}|}^{3}}} where This
24585-820: The other charge (the source charge) E 1 ( r 0 ) = F 01 q 0 = q 1 4 π ε 0 r ^ 01 | r 01 | 2 = q 1 4 π ε 0 r 01 | r 01 | 3 {\displaystyle \mathbf {E} _{1}(\mathbf {r} _{0})={\frac {\mathbf {F} _{01}}{q_{0}}}={\frac {q_{1}}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}_{01} \over {|\mathbf {r} _{01}|}^{2}}={\frac {q_{1}}{4\pi \varepsilon _{0}}}{\mathbf {r} _{01} \over {|\mathbf {r} _{01}|}^{3}}} where This
24750-529: The presence of matter, it is helpful to extend the notion of the electric field into three vector fields: D = ε 0 E + P {\displaystyle \mathbf {D} =\varepsilon _{0}\mathbf {E} +\mathbf {P} } where P is the electric polarization – the volume density of electric dipole moments , and D is the electric displacement field . Since E and P are defined separately, this equation can be used to define D . The physical interpretation of D
24915-529: The presence of matter, it is helpful to extend the notion of the electric field into three vector fields: D = ε 0 E + P {\displaystyle \mathbf {D} =\varepsilon _{0}\mathbf {E} +\mathbf {P} } where P is the electric polarization – the volume density of electric dipole moments , and D is the electric displacement field . Since E and P are defined separately, this equation can be used to define D . The physical interpretation of D
25080-472: The question of whether magnetic fields interacted with the conductors or the electric current, and reasoned that if the force was specifically acting on the current, it should crowd current to one side of the wire, producing a small measurable voltage. In 1879, he discovered this Hall effect while he was working on his doctoral degree at Johns Hopkins University in Baltimore , Maryland . Eighteen years before
25245-556: The region, there is no position dependence: D ( r ) = ε E ( r ) . {\displaystyle \mathbf {D} (\mathbf {r} )=\varepsilon \mathbf {E} (\mathbf {r} ).} For inhomogeneous materials, there is a position dependence throughout the material: D ( r ) = ε ( r ) E ( r ) {\displaystyle \mathbf {D} (\mathbf {r} )=\varepsilon (\mathbf {r} )\mathbf {E} (\mathbf {r} )} For anisotropic materials
25410-556: The region, there is no position dependence: D ( r ) = ε E ( r ) . {\displaystyle \mathbf {D} (\mathbf {r} )=\varepsilon \mathbf {E} (\mathbf {r} ).} For inhomogeneous materials, there is a position dependence throughout the material: D ( r ) = ε ( r ) E ( r ) {\displaystyle \mathbf {D} (\mathbf {r} )=\varepsilon (\mathbf {r} )\mathbf {E} (\mathbf {r} )} For anisotropic materials
25575-416: The same. Because these forces are exerted mutually, two charges must be present for the forces to take place. The electric field of a single charge (or group of charges) describes their capacity to exert such forces on another charged object. These forces are described by Coulomb's law , which says that the greater the magnitude of the charges, the greater the force, and the greater the distance between them,
25740-447: The simply connected specimen. It depends only on the current injected from within the void. Superposition of these two forms of the effect, the ordinary and void effects, can also be realized. First imagine the "ordinary" configuration, a simply connected (void-less) thin rectangular homogeneous element with current-contacts on the (external) boundary. This develops a Hall voltage, in a perpendicular magnetic field. Next, imagine placing
25905-435: The source charge were doubled, the electric field would double, and if you move twice as far away from the source, the field at that point would be only one-quarter its original strength. The electric field can be visualized with a set of lines whose direction at each point is the same as those of the field, a concept introduced by Michael Faraday , whose term ' lines of force ' is still sometimes used. This illustration has
26070-419: The source's rest frame given by Coulomb's law and assigning electric field and magnetic field by their definition given by the form of Lorentz force . However the following equation is only applicable when no acceleration is involved in the particle's history where Coulomb's law can be considered or symmetry arguments can be used for solving Maxwell's equations in a simple manner. The electric field of such
26235-419: The source's rest frame given by Coulomb's law and assigning electric field and magnetic field by their definition given by the form of Lorentz force . However the following equation is only applicable when no acceleration is involved in the particle's history where Coulomb's law can be considered or symmetry arguments can be used for solving Maxwell's equations in a simple manner. The electric field of such
26400-424: The source, the field at that point would be only one-quarter its original strength. The electric field can be visualized with a set of lines whose direction at each point is the same as those of the field, a concept introduced by Michael Faraday , whose term ' lines of force ' is still sometimes used. This illustration has the useful property that, when drawn so that each line represents the same amount of flux ,
26565-483: The straight path and the applied magnetic field. The separation of charge establishes an electric field that opposes the migration of further charge, so a steady electric potential is established for as long as the charge is flowing. In classical electromagnetism electrons move in the opposite direction of the current I (by convention "current" describes a theoretical "hole flow"). In some metals and semiconductors it appears "holes" are actually flowing because
26730-1126: The theory is more complex, because in these materials conduction can involve significant, simultaneous contributions from both electrons and holes , which may be present in different concentrations and have different mobilities . For moderate magnetic fields the Hall coefficient is R H = p μ h 2 − n μ e 2 e ( p μ h + n μ e ) 2 {\displaystyle R_{\mathrm {H} }={\frac {p\mu _{\mathrm {h} }^{2}-n\mu _{\mathrm {e} }^{2}}{e(p\mu _{\mathrm {h} }+n\mu _{\mathrm {e} })^{2}}}} or equivalently R H = p − n b 2 e ( p + n b ) 2 {\displaystyle R_{\mathrm {H} }={\frac {p-nb^{2}}{e(p+nb)^{2}}}} with b = μ e μ h . {\displaystyle b={\frac {\mu _{\mathrm {e} }}{\mu _{\mathrm {h} }}}.} Here n
26895-451: The useful property that, when drawn so that each line represents the same amount of flux , the strength of the field is proportional to the density of the lines. Field lines due to stationary charges have several important properties, including that they always originate from positive charges and terminate at negative charges, they enter all good conductors at right angles, and they never cross or close in on themselves. The field lines are
27060-447: The way that the gravitational field acts between two masses , as they both obey an inverse-square law with distance. This is the basis for Coulomb's law , which states that, for stationary charges, the electric field varies with the source charge and varies inversely with the square of the distance from the source. This means that if the source charge were doubled, the electric field would double, and if you move twice as far away from
27225-413: The weaker the force. Thus, we may informally say that the greater the charge of an object, the stronger its electric field. Similarly, an electric field is stronger nearer charged objects and weaker further away. Electric fields originate from electric charges and time-varying electric currents . Electric fields and magnetic fields are both manifestations of the electromagnetic field , Electromagnetism
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