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86-549: The name of the building is a pun: it can mean dipole in Finnish , but also "the second Poly", the second building of the polytechnic students. The original Polytechnic Students' Union , now called the "Old Poly" ( Finnish : Vanha Poli ), was a National Romantic building located on Lönnrotinkatu in Helsinki that was left behind when the university moved to Otaniemi . Helsinki University of Technology moved from Helsinki to Espoo in

172-409: A magnetic dipole , which generates a magnetic field. The physical chemist Peter J. W. Debye was the first scientist to study molecular dipoles extensively, and, as a consequence, dipole moments are measured in the non- SI unit named debye in his honor. For molecules there are three types of dipoles: More generally, an induced dipole of any polarizable charge distribution ρ (remember that

258-473: A magnetic monopole is a hypothetical particle (or class of particles) that physically has only one magnetic pole (either a north pole or a south pole). In other words, it would possess a "magnetic charge" analogous to an electric charge. Magnetic field lines would start or end on magnetic monopoles, so if they exist, they would give exceptions to the rule that magnetic field lines neither start nor end. Some theories (such as Grand Unified Theories ) have predicted

344-459: A magnetometer . Important classes of magnetometers include using induction magnetometers (or search-coil magnetometers) which measure only varying magnetic fields, rotating coil magnetometers , Hall effect magnetometers, NMR magnetometers , SQUID magnetometers , and fluxgate magnetometers . The magnetic fields of distant astronomical objects are measured through their effects on local charged particles. For instance, electrons spiraling around

430-438: A bar magnet points north. However, that means that Earth's geomagnetic north pole is the south pole (south-seeking pole) of its dipole moment and vice versa. The only known mechanisms for the creation of magnetic dipoles are by current loops or quantum-mechanical spin since the existence of magnetic monopoles has never been experimentally demonstrated. A physical dipole consists of two equal and opposite point charges: in

516-454: A dipole can be found from the gradient of this potential: This is of the same form of the expression for the magnetic field of a point magnetic dipole, ignoring the delta function. In a real electric dipole, however, the charges are physically separate and the electric field diverges or converges at the point charges. This is different to the magnetic field of a real magnetic dipole which is continuous everywhere. The delta function represents

602-422: A dipole moment p 0 along the ẑ direction of the form In vacuum, the exact field produced by this oscillating dipole can be derived using the retarded potential formulation as: Magnetic field A magnetic field (sometimes called B-field ) is a physical field that describes the magnetic influence on moving electric charges , electric currents , and magnetic materials. A moving charge in

688-419: A field line produce synchrotron radiation that is detectable in radio waves . The finest precision for a magnetic field measurement was attained by Gravity Probe B at 5 aT ( 5 × 10  T ). The field can be visualized by a set of magnetic field lines , that follow the direction of the field at each point. The lines can be constructed by measuring the strength and direction of the magnetic field at

774-409: A large number of points (or at every point in space). Then, mark each location with an arrow (called a vector ) pointing in the direction of the local magnetic field with its magnitude proportional to the strength of the magnetic field. Connecting these arrows then forms a set of magnetic field lines. The direction of the magnetic field at any point is parallel to the direction of nearby field lines, and

860-420: A magnetic H -field is produced by fictitious magnetic charges that are spread over the surface of each pole. These magnetic charges are in fact related to the magnetization field M . The H -field, therefore, is analogous to the electric field E , which starts at a positive electric charge and ends at a negative electric charge. Near the north pole, therefore, all H -field lines point away from

946-648: A magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet 's magnetic field pulls on ferromagnetic materials such as iron , and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism , diamagnetism , and antiferromagnetism , although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of

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1032-494: A magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field (more precisely, a pseudovector field). In electromagnetics , the term magnetic field is used for two distinct but closely related vector fields denoted by the symbols B and H . In the International System of Units , the unit of B , magnetic flux density,

1118-424: A magnetized material, the quantities on each side of this equation differ by the magnetization field of the material. Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin . Magnetic fields and electric fields are interrelated and are both components of the electromagnetic force , one of

1204-429: A magnetized object is divided in half, a new pole appears on the surface of each piece, so each has a pair of complementary poles. The magnetic pole model does not account for magnetism that is produced by electric currents, nor the inherent connection between angular momentum and magnetism. The pole model usually treats magnetic charge as a mathematical abstraction, rather than a physical property of particles. However,

1290-463: A molecule has a charge distribution) is caused by an electric field external to ρ . This field may, for instance, originate from an ion or polar molecule in the vicinity of ρ or may be macroscopic (e.g., a molecule between the plates of a charged capacitor ). The size of the induced dipole moment is equal to the product of the strength of the external field and the dipole polarizability of ρ . Dipole moment values can be obtained from measurement of

1376-507: A non-degenerate state (see degenerate energy level ) is given as the expectation (average) value of the dipole operator, where | S ⟩ {\displaystyle |\,S\,\rangle } is an S -state, non-degenerate, wavefunction, which is symmetric or antisymmetric under inversion: I | S ⟩ = ± | S ⟩ {\displaystyle {\mathfrak {I}}\,|\,S\,\rangle =\pm |\,S\,\rangle } . Since

1462-402: A north and a south pole. The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The magnetic field of a small straight magnet is proportional to the magnet's strength (called its magnetic dipole moment m ). The equations are non-trivial and depend on the distance from the magnet and the orientation of the magnet. For simple magnets, m points in

1548-416: A positive charge and toward a negative charge. When placed in a homogeneous electric or magnetic field , equal but opposite forces arise on each side of the dipole creating a torque τ }: for an electric dipole moment p (in coulomb-meters), or for a magnetic dipole moment m (in ampere-square meters). The resulting torque will tend to align the dipole with the applied field, which in

1634-500: A small distance vector d , such that m = q m   d . The magnetic pole model predicts correctly the field H both inside and outside magnetic materials, in particular the fact that H is opposite to the magnetization field M inside a permanent magnet. Since it is based on the fictitious idea of a magnetic charge density , the pole model has limitations. Magnetic poles cannot exist apart from each other as electric charges can, but always come in north–south pairs. If

1720-452: A small magnet is proportional both to the applied magnetic field and to the magnetic moment m of the magnet: τ = m × B = μ 0 m × H , {\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} =\mu _{0}\mathbf {m} \times \mathbf {H} ,\,} where × represents the vector cross product . This equation includes all of

1806-408: A torque proportional to the distance (perpendicular to the force) between them. With the definition of m as the pole strength times the distance between the poles, this leads to τ = μ 0 m H sin  θ , where μ 0 is a constant called the vacuum permeability , measuring 4π × 10 V · s /( A · m ) and θ is the angle between H and m . Mathematically, the torque τ on

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1892-450: A zero permanent dipole. This fact follows quantum mechanically from the inversion symmetry of atoms. All 3 components of the dipole operator are antisymmetric under inversion with respect to the nucleus, where p {\displaystyle {\mathfrak {p}}} is the dipole operator and I {\displaystyle {\mathfrak {I}}} is the inversion operator. The permanent dipole moment of an atom in

1978-501: Is tesla (symbol: T). The Gaussian-cgs unit of B is the gauss (symbol: G). (The conversion is 1 T ≘ 10000 G. ) One nanotesla corresponds to 1 gamma (symbol: γ). The magnetic H field is defined: H ≡ 1 μ 0 B − M {\displaystyle \mathbf {H} \equiv {\frac {1}{\mu _{0}}}\mathbf {B} -\mathbf {M} } where μ 0 {\displaystyle \mu _{0}}

2064-552: Is a specific example of a general rule that magnets are attracted (or repulsed depending on the orientation of the magnet) into regions of higher magnetic field. Any non-uniform magnetic field, whether caused by permanent magnets or electric currents, exerts a force on a small magnet in this way. The details of the Amperian loop model are different and more complicated but yield the same result: that magnetic dipoles are attracted/repelled into regions of higher magnetic field. Mathematically,

2150-406: Is an electromagnetic phenomenon which occurs in two ways: Dipoles, whether electric or magnetic, can be characterized by their dipole moment, a vector quantity. For the simple electric dipole, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges. (To be precise: for

2236-491: Is in the opposite direction. If both the speed and the charge are reversed then the direction of the force remains the same. For that reason a magnetic field measurement (by itself) cannot distinguish whether there is a positive charge moving to the right or a negative charge moving to the left. (Both of these cases produce the same current.) On the other hand, a magnetic field combined with an electric field can distinguish between these, see Hall effect below. The first term in

2322-417: Is no net force on that magnet since the force is opposite for opposite poles. If, however, the magnetic field of the first magnet is nonuniform (such as the H near one of its poles), each pole of the second magnet sees a different field and is subject to a different force. This difference in the two forces moves the magnet in the direction of increasing magnetic field and may also cause a net torque. This

2408-422: Is particularly true for magnetic fields, such as those due to electric currents, that are not generated by magnetic materials. A realistic model of magnetism is more complicated than either of these models; neither model fully explains why materials are magnetic. The monopole model has no experimental support. The Amperian loop model explains some, but not all of a material's magnetic moment. The model predicts that

2494-413: Is still regularly used for conventions, congresses and student parties. The building houses over 20 conference rooms and auditoriums. Dipoli was owned by the student union of Aalto University until 2013 when it was announced that the building would be sold to the university itself for an undisclosed sum. The building was extensively renovated between 2015 and 2017 turning it into the new main building for

2580-449: Is strictly only valid for magnets of zero size, but is often a good approximation for not too large magnets. The magnetic force on larger magnets is determined by dividing them into smaller regions each having their own m then summing up the forces on each of these very small regions . If two like poles of two separate magnets are brought near each other, and one of the magnets is allowed to turn, it promptly rotates to align itself with

2666-418: Is that of maximum increase of m · B . The dot product m · B = mB cos( θ ) , where m and B represent the magnitude of the m and B vectors and θ is the angle between them. If m is in the same direction as B then the dot product is positive and the gradient points "uphill" pulling the magnet into regions of higher B -field (more strictly larger m · B ). This equation

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2752-473: Is the atomic number of the i  th nucleus. The dipole observable (physical quantity) has the quantum mechanical dipole operator : Notice that this definition is valid only for neutral atoms or molecules, i.e. total charge equal to zero. In the ionized case, we have where r c {\displaystyle \mathbf {r} _{c}} is the center of mass of the molecule/group of particles. A non-degenerate ( S -state) atom can have only

2838-547: Is the tesla (in SI base units: kilogram per second squared per ampere), which is equivalent to newton per meter per ampere. The unit of H , magnetic field strength, is ampere per meter (A/m). B and H differ in how they take the medium and/or magnetization into account. In vacuum , the two fields are related through the vacuum permeability , B / μ 0 = H {\displaystyle \mathbf {B} /\mu _{0}=\mathbf {H} } ; in

2924-446: Is the vacuum permeability , and M is the magnetization vector . In a vacuum, B and H are proportional to each other. Inside a material they are different (see H and B inside and outside magnetic materials ). The SI unit of the H -field is the ampere per metre (A/m), and the CGS unit is the oersted (Oe). An instrument used to measure the local magnetic field is known as

3010-471: The Barnett effect or magnetization by rotation . Rotating the loop faster (in the same direction) increases the current and therefore the magnetic moment, for example. Specifying the force between two small magnets is quite complicated because it depends on the strength and orientation of both magnets and their distance and direction relative to each other. The force is particularly sensitive to rotations of

3096-420: The dielectric constant . Some typical gas phase values given with the unit debye are: Potassium bromide (KBr) has one of the highest dipole moments because it is an ionic compound that exists as a molecule in the gas phase. The overall dipole moment of a molecule may be approximated as a vector sum of bond dipole moments . As a vector sum it depends on the relative orientation of the bonds, so that from

3182-409: The multipole expansion is precisely the point dipole field. Although there are no known magnetic monopoles in nature, there are magnetic dipoles in the form of the quantum-mechanical spin associated with particles such as electrons (although the accurate description of such effects falls outside of classical electromagnetism). A theoretical magnetic point dipole has a magnetic field of exactly

3268-448: The right hand grip rule ), with a magnitude equal to the current in the loop times the area of the loop. Similar to magnetic current loops, the electron particle and some other fundamental particles have magnetic dipole moments, as an electron generates a magnetic field identical to that generated by a very small current loop. However, an electron's magnetic dipole moment is not due to a current loop, but to an intrinsic property of

3354-444: The z -axis. Then, The field itself is a vector quantity: where This is exactly the field of a point dipole, exactly the dipole term in the multipole expansion of an arbitrary field, and approximately the field of any dipole-like configuration at large distances. The vector potential A of a magnetic dipole is with the same definitions as above. The electrostatic potential at position r due to an electric dipole at

3440-583: The "magnetic field" written B and H . While both the best names for these fields and exact interpretation of what these fields represent has been the subject of long running debate, there is wide agreement about how the underlying physics work. Historically, the term "magnetic field" was reserved for H while using other terms for B , but many recent textbooks use the term "magnetic field" to describe B as well as or in place of H . There are many alternative names for both (see sidebars). The magnetic field vector B at any point can be defined as

3526-600: The "number" of field lines through a surface. These concepts can be quickly "translated" to their mathematical form. For example, the number of field lines through a given surface is the surface integral of the magnetic field. Various phenomena "display" magnetic field lines as though the field lines were physical phenomena. For example, iron filings placed in a magnetic field form lines that correspond to "field lines". Magnetic field "lines" are also visually displayed in polar auroras , in which plasma particle dipole interactions create visible streaks of light that line up with

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3612-460: The Earth's magnetic field, they are respectively "north-seeking" and "south-seeking" poles: if the magnet were freely suspended in the Earth's magnetic field, the north-seeking pole would point towards the north and the south-seeking pole would point towards the south. The dipole moment of the bar magnet points from its magnetic south to its magnetic north pole . In a magnetic compass , the north pole of

3698-467: The Hermitian adjoint I ∗ {\displaystyle {\mathfrak {I}}^{*}\,} may be moved from bra to ket and then becomes I ∗ ∗ = I {\displaystyle {\mathfrak {I}}^{**}={\mathfrak {I}}\,} . Since the only quantity that is equal to minus itself is the zero, the expectation value vanishes, In

3784-511: The Lewis structures for the resonance forms of ozone which show a positive charge on the central oxygen atom. An example in organic chemistry of the role of geometry in determining dipole moment is the cis and trans isomers of 1,2-dichloroethene . In the cis isomer the two polar C−Cl bonds are on the same side of the C=C double bond and the molecular dipole moment is 1.90 D. In the trans isomer,

3870-586: The Lorentz equation is from the theory of electrostatics , and says that a particle of charge q in an electric field E experiences an electric force: F electric = q E . {\displaystyle \mathbf {F} _{\text{electric}}=q\mathbf {E} .} The second term is the magnetic force: F magnetic = q ( v × B ) . {\displaystyle \mathbf {F} _{\text{magnetic}}=q(\mathbf {v} \times \mathbf {B} ).} Using

3956-522: The area of the loop and depends on the direction of the current using the right-hand rule. An ideal magnetic dipole is modeled as a real magnetic dipole whose area a has been reduced to zero and its current I increased to infinity such that the product m = Ia is finite. This model clarifies the connection between angular momentum and magnetic moment, which is the basis of the Einstein–de Haas effect rotation by magnetization and its inverse,

4042-425: The case of an electric dipole, yields a potential energy of The energy of a magnetic dipole is similarly In addition to dipoles in electrostatics, it is also common to consider an electric or magnetic dipole that is oscillating in time. It is an extension, or a more physical next-step, to spherical wave radiation. In particular, consider a harmonically oscillating electric dipole, with angular frequency ω and

4128-430: The case of open-shell atoms with degenerate energy levels, one could define a dipole moment by the aid of the first-order Stark effect . This gives a non-vanishing dipole (by definition proportional to a non-vanishing first-order Stark shift) only if some of the wavefunctions belonging to the degenerate energies have opposite parity ; i.e., have different behavior under inversion. This is a rare occurrence, but happens for

4214-448: The charge carriers in a material through the Hall effect . The Earth produces its own magnetic field , which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass . The force on an electric charge depends on its location, speed, and direction; two vector fields are used to describe this force. The first is the electric field , which describes

4300-403: The definition of the cross product, the magnetic force can also be written as a scalar equation: F magnetic = q v B sin ⁡ ( θ ) {\displaystyle F_{\text{magnetic}}=qvB\sin(\theta )} where F magnetic , v , and B are the scalar magnitude of their respective vectors, and θ is the angle between the velocity of

4386-406: The definition of the dipole moment, one should always consider the "dipole limit", where, for example, the distance of the generating charges should converge to 0 while simultaneously, the charge strength should diverge to infinity in such a way that the product remains a positive constant.) For the magnetic (dipole) current loop, the magnetic dipole moment points through the loop (according to

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4472-533: The dipole moment information can be deduced about the molecular geometry . For example, the zero dipole of CO 2 implies that the two C=O bond dipole moments cancel so that the molecule must be linear. For H 2 O the O−H bond moments do not cancel because the molecule is bent. For ozone (O 3 ) which is also a bent molecule, the bond dipole moments are not zero even though the O−O bonds are between similar atoms. This agrees with

4558-406: The dipole moment is zero because the two C−Cl bonds are on opposite sides of the C=C and cancel (and the two bond moments for the much less polar C−H bonds also cancel). Another example of the role of molecular geometry is boron trifluoride , which has three polar bonds with a difference in electronegativity greater than the traditionally cited threshold of 1.7 for ionic bonding . However, due to

4644-428: The direction of a line drawn from the south to the north pole of the magnet. Flipping a bar magnet is equivalent to rotating its m by 180 degrees. The magnetic field of larger magnets can be obtained by modeling them as a collection of a large number of small magnets called dipoles each having their own m . The magnetic field produced by the magnet then is the net magnetic field of these dipoles; any net force on

4730-464: The early 1960s, with the first buildings to be constructed designed by architect Alvar Aalto . In 1961 an architecture competition was held for what would become the new building for the Student Union of the university. Due to the challenging rocky location and adaptability requirements none of the competition entries fulfilled all the jury's demands and the first prize was not awarded: the second prize

4816-437: The electron. The electron may also have an electric dipole moment though such has yet to be observed (see electron electric dipole moment ). A permanent magnet, such as a bar magnet, owes its magnetism to the intrinsic magnetic dipole moment of the electron. The two ends of a bar magnet are referred to as poles (not to be confused with monopoles , see Classification below) and may be labeled "north" and "south". In terms of

4902-425: The equilateral triangular distribution of the fluoride ions centered on and in the same plane as the boron cation, the symmetry of the molecule results in its dipole moment being zero. Consider a collection of N particles with charges q i and position vectors r i . For instance, this collection may be a molecule consisting of electrons, all with charge − e , and nuclei with charge eZ i , where Z i

4988-409: The excited H-atom, where 2s and 2p states are "accidentally" degenerate (see article Laplace–Runge–Lenz vector for the origin of this degeneracy) and have opposite parity (2s is even and 2p is odd). The far-field strength, B , of a dipole magnetic field is given by where Conversion to cylindrical coordinates is achieved using r = z + ρ and where ρ is the perpendicular distance from

5074-408: The existence of magnetic monopoles, but so far, none have been observed. In the model developed by Ampere , the elementary magnetic dipole that makes up all magnets is a sufficiently small Amperian loop with current I and loop area A . The dipole moment of this loop is m = IA . These magnetic dipoles produce a magnetic B -field. The magnetic field of a magnetic dipole is depicted in

5160-411: The figure. From outside, the ideal magnetic dipole is identical to that of an ideal electric dipole of the same strength. Unlike the electric dipole, a magnetic dipole is properly modeled as a current loop having a current I and an area a . Such a current loop has a magnetic moment of m = I a , {\displaystyle m=Ia,} where the direction of m is perpendicular to

5246-522: The first. In this example, the magnetic field of the stationary magnet creates a magnetic torque on the magnet that is free to rotate. This magnetic torque τ tends to align a magnet's poles with the magnetic field lines. A compass, therefore, turns to align itself with Earth's magnetic field. In terms of the pole model, two equal and opposite magnetic charges experiencing the same H also experience equal and opposite forces. Since these equal and opposite forces are in different locations, this produces

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5332-546: The force acting on a stationary charge and gives the component of the force that is independent of motion. The magnetic field, in contrast, describes the component of the force that is proportional to both the speed and direction of charged particles. The field is defined by the Lorentz force law and is, at each instant, perpendicular to both the motion of the charge and the force it experiences. There are two different, but closely related vector fields which are both sometimes called

5418-515: The force and torques between two magnets as due to magnetic poles repelling or attracting each other in the same manner as the Coulomb force between electric charges. At the microscopic level, this model contradicts the experimental evidence, and the pole model of magnetism is no longer the typical way to introduce the concept. However, it is still sometimes used as a macroscopic model for ferromagnetism due to its mathematical simplicity. In this model,

5504-408: The force on a small magnet having a magnetic moment m due to a magnetic field B is: F = ∇ ( m ⋅ B ) , {\displaystyle \mathbf {F} ={\boldsymbol {\nabla }}\left(\mathbf {m} \cdot \mathbf {B} \right),} where the gradient ∇ is the change of the quantity m · B per unit distance and the direction

5590-474: The force on the particle when its velocity is v ; repeat with v in some other direction. Now find a B that makes the Lorentz force law fit all these results—that is the magnetic field at the place in question. The B field can also be defined by the torque on a magnetic dipole, m . τ = m × B {\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} } The SI unit of B

5676-414: The four fundamental forces of nature. Magnetic fields are used throughout modern technology, particularly in electrical engineering and electromechanics . Rotating magnetic fields are used in both electric motors and generators . The interaction of magnetic fields in electric devices such as transformers is conceptualized and investigated as magnetic circuits . Magnetic forces give information about

5762-519: The given configuration. This is simply one term in the multipole expansion when the total charge ("monopole moment") is 0—as it always is for the magnetic case, since there are no magnetic monopoles. The dipole term is the dominant one at large distances: Its field falls off in proportion to ⁠ 1 / r ⁠ , as compared to ⁠ 1 / r ⁠ for the next ( quadrupole ) term and higher powers of ⁠ 1 / r ⁠ for higher terms, or ⁠ 1 / r ⁠ for

5848-399: The literal sense, two poles. Its field at large distances (i.e., distances large in comparison to the separation of the poles) depends almost entirely on the dipole moment as defined above. A point (electric) dipole is the limit obtained by letting the separation tend to 0 while keeping the dipole moment fixed. The field of a point dipole has a particularly simple form, and the order-1 term in

5934-432: The local density of field lines can be made proportional to its strength. Magnetic field lines are like streamlines in fluid flow , in that they represent a continuous distribution, and a different resolution would show more or fewer lines. An advantage of using magnetic field lines as a representation is that many laws of magnetism (and electromagnetism) can be stated completely and concisely using simple concepts such as

6020-763: The local direction of Earth's magnetic field. Field lines can be used as a qualitative tool to visualize magnetic forces. In ferromagnetic substances like iron and in plasmas, magnetic forces can be understood by imagining that the field lines exert a tension , (like a rubber band) along their length, and a pressure perpendicular to their length on neighboring field lines. "Unlike" poles of magnets attract because they are linked by many field lines; "like" poles repel because their field lines do not meet, but run parallel, pushing on each other. Permanent magnets are objects that produce their own persistent magnetic fields. They are made of ferromagnetic materials, such as iron and nickel , that have been magnetized, and they have both

6106-460: The magnet is a result of adding up the forces on the individual dipoles. There are two simplified models for the nature of these dipoles: the magnetic pole model and the Amperian loop model . These two models produce two different magnetic fields, H and B . Outside a material, though, the two are identical (to a multiplicative constant) so that in many cases the distinction can be ignored. This

6192-413: The magnets due to magnetic torque. The force on each magnet depends on its magnetic moment and the magnetic field of the other. To understand the force between magnets, it is useful to examine the magnetic pole model given above. In this model, the H -field of one magnet pushes and pulls on both poles of a second magnet. If this H -field is the same at both poles of the second magnet then there

6278-400: The monopole term. Many molecules have such dipole moments due to non-uniform distributions of positive and negative charges on the various atoms. Such is the case with polar compounds like hydrogen fluoride (HF), where electron density is shared unequally between atoms. Therefore, a molecule's dipole is an electric dipole with an inherent electric field that should not be confused with

6364-449: The motion of electrons within an atom are connected to those electrons' orbital magnetic dipole moment , and these orbital moments do contribute to the magnetism seen at the macroscopic level. However, the motion of electrons is not classical, and the spin magnetic moment of electrons (which is not explained by either model) is also a significant contribution to the total moment of magnets. Historically, early physics textbooks would model

6450-444: The north pole (whether inside the magnet or out) while near the south pole all H -field lines point toward the south pole (whether inside the magnet or out). Too, a north pole feels a force in the direction of the H -field while the force on the south pole is opposite to the H -field. In the magnetic pole model, the elementary magnetic dipole m is formed by two opposite magnetic poles of pole strength q m separated by

6536-400: The origin is given by: where p is the (vector) dipole moment , and є 0 is the permittivity of free space . This term appears as the second term in the multipole expansion of an arbitrary electrostatic potential Φ( r ). If the source of Φ( r ) is a dipole, as it is assumed here, this term is the only non-vanishing term in the multipole expansion of Φ( r ). The electric field from

6622-442: The particle and the magnetic field. The vector B is defined as the vector field necessary to make the Lorentz force law correctly describe the motion of a charged particle. In other words, [T]he command, "Measure the direction and magnitude of the vector B at such and such a place," calls for the following operations: Take a particle of known charge q . Measure the force on q at rest, to determine E . Then measure

6708-420: The particle's velocity , and × denotes the cross product . The direction of force on the charge can be determined by a mnemonic known as the right-hand rule (see the figure). Using the right hand, pointing the thumb in the direction of the current, and the fingers in the direction of the magnetic field, the resulting force on the charge points outwards from the palm. The force on a negatively charged particle

6794-525: The product of the wavefunction (in the ket) and its complex conjugate (in the bra) is always symmetric under inversion and its inverse, it follows that the expectation value changes sign under inversion. We used here the fact that I {\displaystyle {\mathfrak {I}}} , being a symmetry operator, is unitary : I − 1 = I ∗ {\displaystyle {\mathfrak {I}}^{-1}={\mathfrak {I}}^{*}\,} and by definition

6880-431: The same form as the electric field of an electric point dipole. A very small current-carrying loop is approximately a magnetic point dipole; the magnetic dipole moment of such a loop is the product of the current flowing in the loop and the (vector) area of the loop. Any configuration of charges or currents has a 'dipole moment', which describes the dipole whose field is the best approximation, at large distances, to that of

6966-456: The site as possible; but blasting the hard granite base rock inevitably fragmented it. The building is seen as a key example of organic architecture. Reima Pietilä himself said of the building: "As in Samuel Beckett's novels, there are no exposed trenchmarks of balance. The concept of a traditional balance of composition is redundant in the design aesthetics of Dipoli. (...) after the hill top

7052-451: The strong field pointing in the opposite direction between the point charges, which is often omitted since one is rarely interested in the field at the dipole's position. For further discussions about the internal field of dipoles, see or Magnetic moment § Internal magnetic field of a dipole . Since the direction of an electric field is defined as the direction of the force on a positive charge, electric field lines point away from

7138-454: The university. The refurbished building includes an auditorium, restaurants and exhibitions spaces. The university's management also works in Dipoli. The building uses extensively materials from Finnish nature, such as pine wood, copper, and natural rocks. Dipoli has 500 windows of which only four are identical. The architects originally planned for as little interference with the natural granite of

7224-401: The vector that, when used in the Lorentz force law , correctly predicts the force on a charged particle at that point: F = q E + q ( v × B ) {\displaystyle \mathbf {F} =q\mathbf {E} +q(\mathbf {v} \times \mathbf {B} )} Here F is the force on the particle, q is the particle's electric charge , v , is

7310-399: Was blasted the broken heaps of rock gave an initial image which one could follow with the slow, crawling motion of structure. The reptilian metaphoric image: the silhouetted dinosaur accentuating the rhythmic consistency of retardation." Dipole In physics , a dipole (from Ancient Greek δίς ( dís )  'twice' and πόλος ( pólos )  'axis')

7396-487: Was shared by the architect couple Reima and Raili Pietilä and Osmo Lappo, who were asked to further develop their proposals. Finally, the design by the Pietiläs was chosen as the basis for the new building. Construction work began in 1965, and the building was ready for use in autumn 1966. In 1993 the building was transformed into a training centre for the university due to high maintenance costs. Besides its primary role, Dipoli

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