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51-717: One volt is defined as the electric potential between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points. It can be expressed in terms of SI base units ( m , kg , s , and A ) as Equivalently, it is the potential difference between two points that will impart one joule of energy per coulomb of charge that passes through it. It can be expressed in terms of SI base units ( m , kg , s , and A ) as It can also be expressed as amperes times ohms (current times resistance, Ohm's law ), webers per second (magnetic flux per time), watts per ampere (power per current), or joules per coulomb (energy per charge), which

102-427: A battery is determined by the chemistry of that cell (see Galvanic cell § Cell voltage ). Cells can be combined in series for multiples of that voltage, or additional circuitry added to adjust the voltage to a different level. Mechanical generators can usually be constructed to any voltage in a range of feasibility. Nominal voltages of familiar sources: In 1800, as the result of a professional disagreement over

153-541: A changing magnetic field ; see Maxwell's equations ). The generalization of electric potential to this case is described in the section § Generalization to electrodynamics . The electric potential arising from a point charge, Q , at a distance, r , from the location of Q is observed to be V E = 1 4 π ε 0 Q r , {\displaystyle V_{\mathbf {E} }={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Q}{r}},} where ε 0

204-515: A charged object, if the object has a positive charge, the force will be in the direction of the electric field vector at the location of the charge; if the charge is negative, the force will be in the opposite direction. The magnitude of force is given by the quantity of the charge multiplied by the magnitude of the electric field vector, | F | = q | E | . {\displaystyle |\mathbf {F} |=q|\mathbf {E} |.} An electric potential at

255-411: A point r in a static electric field E is given by the line integral V E = − ∫ C E ⋅ d ℓ {\displaystyle V_{\mathbf {E} }=-\int _{\mathcal {C}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}\,} where C is an arbitrary path from some fixed reference point to r ; it

306-440: A ratio because the cgs unit of voltage is inconveniently small and one volt in this definition is approximately the emf of a Daniell cell , the standard source of voltage in the telegraph systems of the day. At that time, the volt was defined as the potential difference [i.e., what is nowadays called the "voltage (difference)"] across a conductor when a current of one ampere dissipates one watt of power. The "international volt"

357-531: A series-connected array of several thousand or tens of thousands of junctions , excited by microwave signals between 10 and 80 GHz (depending on the array design). Empirically, several experiments have shown that the method is independent of device design, material, measurement setup, etc., and no correction terms are required in a practical implementation. In the water-flow analogy , sometimes used to explain electric circuits by comparing them with water-filled pipes, voltage (difference in electric potential)

408-411: A spatial derivative of a discontinuous electric potential yields an electric field of impossibly infinite magnitude. Notably, the electric potential due to an idealized point charge (proportional to 1 ⁄ r , with r the distance from the point charge) is continuous in all space except at the location of the point charge. Though electric field is not continuous across an idealized surface charge , it

459-532: Is a retarded potential that propagates at the speed of light and is the solution to an inhomogeneous wave equation : ∇ 2 V − 1 c 2 ∂ 2 V ∂ t 2 = − ρ ε 0 {\displaystyle \nabla ^{2}V-{\frac {1}{c^{2}}}{\frac {\partial ^{2}V}{\partial t^{2}}}=-{\frac {\rho }{\varepsilon _{0}}}} The SI derived unit of electric potential

510-409: Is a vector quantity expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or occasionally φ , equal to the electric potential energy of any charged particle at any location (measured in joules ) divided by the charge of that particle (measured in coulombs ). By dividing out the charge on the particle a quotient is obtained that is a property of

561-414: Is also equivalent to electronvolts per elementary charge : The volt is named after Alessandro Volta . As with every SI unit named for a person, its symbol starts with an upper case letter (V), but when written in full, it follows the rules for capitalisation of a common noun ; i.e., volt becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case. Historically

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612-543: Is canceled by the curl of ∂ A ∂ t {\displaystyle {\frac {\partial \mathbf {A} }{\partial t}}} according to the Maxwell–Faraday equation . One can therefore write E = − ∇ V − ∂ A ∂ t , {\displaystyle \mathbf {E} =-\mathbf {\nabla } V-{\frac {\partial \mathbf {A} }{\partial t}},} where V

663-606: Is likened to difference in water pressure , while current is proportional to the amount of water flowing. A resistor would be a reduced diameter somewhere in the piping or something akin to a radiator offering resistance to flow. The relationship between voltage and current is defined (in ohmic devices like resistors ) by Ohm's law . Ohm's Law is analogous to the Hagen–Poiseuille equation , as both are linear models relating flux and potential in their respective systems. The voltage produced by each electrochemical cell in

714-409: Is negligible. The motion across the field is supposed to proceed with negligible acceleration, so as to avoid the test charge acquiring kinetic energy or producing radiation. By definition, the electric potential at the reference point is zero units. Typically, the reference point is earth or a point at infinity , although any point can be used. In classical electrostatics , the electrostatic field

765-539: Is not infinite at any point. Therefore, the electric potential is continuous across an idealized surface charge. Additionally, an idealized line of charge has electric potential (proportional to ln( r ) , with r the radial distance from the line of charge) is continuous everywhere except on the line of charge. Classical mechanics explores concepts such as force , energy , and potential . Force and potential energy are directly related. A net force acting on any object will cause it to accelerate . As an object moves in

816-494: Is sometimes called the Galvani potential , ϕ . The terms "voltage" and "electric potential" are a bit ambiguous but one may refer to either of these in different contexts. where λ {\displaystyle \lambda } is uniform linear charge density. where σ {\displaystyle \sigma } is uniform surface charge density. where λ {\displaystyle \lambda }

867-566: Is the elementary charge and h is the Planck constant ), a "conventional" value K J-90 = 0.4835979 GHz/μV was used for the purpose of defining the volt. As a consequence of the 2019 revision of the SI , as of 2019 the Josephson constant has an exact value of K J = 483 597 .848 416 98 ... GHz/V , which replaced the conventional value K J-90 . This standard is typically realized using

918-489: Is the permittivity of vacuum , V E is known as the Coulomb potential . Note that, in contrast to the magnitude of an electric field due to a point charge, the electric potential scales respective to the reciprocal of the radius, rather than the radius squared. The electric potential at any location, r , in a system of point charges is equal to the sum of the individual electric potentials due to every point charge in

969-406: Is the volt (in honor of Alessandro Volta ), denoted as V, which is why the electric potential difference between two points in space is known as a voltage . Older units are rarely used today. Variants of the centimetre–gram–second system of units included a number of different units for electric potential, including the abvolt and the statvolt . Inside metals (and other solids and liquids),

1020-625: Is the scalar potential defined by the conservative field F . The electrostatic potential is simply the special case of this definition where A is time-invariant. On the other hand, for time-varying fields, − ∫ a b E ⋅ d ℓ ≠ V ( b ) − V ( a ) {\displaystyle -\int _{a}^{b}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}\neq V_{(b)}-V_{(a)}} unlike electrostatics. The electrostatic potential could have any constant added to it without affecting

1071-459: Is the total charge density and ∇ ⋅ {\textstyle \mathbf {\nabla } \cdot } denotes the divergence . The concept of electric potential is closely linked with potential energy . A test charge , q , has an electric potential energy , U E , given by U E = q V . {\displaystyle U_{\mathbf {E} }=q\,V.} The potential energy and hence, also

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1122-413: Is uniform linear charge density. outside the sphere, where Q {\displaystyle Q} is the total charge uniformly distributed in the volume. inside the sphere, where Q {\displaystyle Q} is the total charge uniformly distributed in the volume. outside the sphere, where Q {\displaystyle Q} is the total charge uniformly distributed on

1173-805: Is uniquely determined up to a constant that is added or subtracted from the integral. In electrostatics, the Maxwell-Faraday equation reveals that the curl ∇ × E {\textstyle \nabla \times \mathbf {E} } is zero, making the electric field conservative . Thus, the line integral above does not depend on the specific path C chosen but only on its endpoints, making V E {\textstyle V_{\mathbf {E} }} well-defined everywhere. The gradient theorem then allows us to write: E = − ∇ V E {\displaystyle \mathbf {E} =-\mathbf {\nabla } V_{\mathbf {E} }\,} This states that

1224-458: The Maxwell-Faraday equation ). Instead, one can still define a scalar potential by also including the magnetic vector potential A . In particular, A is defined to satisfy: B = ∇ × A {\displaystyle \mathbf {B} =\mathbf {\nabla } \times \mathbf {A} } where B is the magnetic field . By the fundamental theorem of vector calculus , such an A can always be found, since

1275-465: The Papal States . The house in which he was born may still be seen on Via Marconi, 25, in the center of Bologna. Domenico was a goldsmith . His family had produced several illustrious men. Galvani then began taking an interest in the field of "medical electricity". This field emerged in the middle of the 18th century, following electrical researches and the discovery of the effects of electricity on

1326-403: The electric field potential , potential drop, the electrostatic potential ) is defined as the amount of work / energy needed per unit of electric charge to move the charge from a reference point to a specific point in an electric field. More precisely, the electric potential is the energy per unit charge for a test charge that is so small that the disturbance of the field under consideration

1377-490: The " conventional " volt, V 90 , defined in 1987 by the 18th General Conference on Weights and Measures and in use from 1990 to 2019, was implemented using the Josephson effect for exact frequency-to-voltage conversion, combined with the caesium frequency standard . Though the Josephson effect is still used to realize a volt, the constant used has changed slightly. For the Josephson constant , K J = 2 e / h (where e

1428-675: The British Association for the Advancement of Science had defined the volt, ohm, and farad. In 1881, the International Electrical Congress, now the International Electrotechnical Commission (IEC), approved the volt as the unit for electromotive force. They made the volt equal to 10 cgs units of voltage, the cgs system at the time being the customary system of units in science. They chose such

1479-402: The body. Volta's intuition was correct. Volta, essentially, objected to Galvani’s conclusions about "animal electric fluid", but the two scientists disagreed respectfully and Volta coined the term "Galvanism" for a direct current of electricity produced by chemical action. Since Galvani was reluctant to intervene in the controversy with Volta, he trusted his nephew, Giovanni Aldini , to act as

1530-415: The conductions were caused by specific electricity intrinsic to the animal's legs or other body parts. Volta believed that the contractions depended on the metal cable Galvani used to connect the nerves and muscles in his experiments. Every cell has a cell potential ; biological electricity has the same chemical underpinnings as the current between electrochemical cells , and thus can be duplicated outside

1581-442: The direction of a force acting on it, its potential energy decreases. For example, the gravitational potential energy of a cannonball at the top of a hill is greater than at the base of the hill. As it rolls downhill, its potential energy decreases and is being translated to motion – kinetic energy . It is possible to define the potential of certain force fields so that the potential energy of an object in that field depends only on

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1632-404: The divergence of the magnetic field is always zero due to the absence of magnetic monopoles . Now, the quantity F = E + ∂ A ∂ t {\displaystyle \mathbf {F} =\mathbf {E} +{\frac {\partial \mathbf {A} }{\partial t}}} is a conservative field, since the curl of E {\displaystyle \mathbf {E} }

1683-442: The electric field cannot be expressed only as a scalar potential . Instead, the electric field can be expressed as both the scalar electric potential and the magnetic vector potential . The electric potential and the magnetic vector potential together form a four-vector , so that the two kinds of potential are mixed under Lorentz transformations . Practically, the electric potential is a continuous function in all space, because

1734-425: The electric field is no longer conservative : ∫ C E ⋅ d ℓ {\displaystyle \textstyle \int _{C}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}} is path-dependent because ∇ × E ≠ 0 {\displaystyle \mathbf {\nabla } \times \mathbf {E} \neq \mathbf {0} } (due to

1785-416: The electric field itself. In short, an electric potential is the electric potential energy per unit charge. This value can be calculated in either a static (time-invariant) or a dynamic (time-varying) electric field at a specific time with the unit joules per coulomb (J⋅C ) or volt (V). The electric potential at infinity is assumed to be zero. In electrodynamics , when time-varying fields are present,

1836-617: The electric field points "downhill" towards lower voltages. By Gauss's law , the potential can also be found to satisfy Poisson's equation : ∇ ⋅ E = ∇ ⋅ ( − ∇ V E ) = − ∇ 2 V E = ρ / ε 0 {\displaystyle \mathbf {\nabla } \cdot \mathbf {E} =\mathbf {\nabla } \cdot \left(-\mathbf {\nabla } V_{\mathbf {E} }\right)=-\nabla ^{2}V_{\mathbf {E} }=\rho /\varepsilon _{0}} where ρ

1887-758: The electric field. In electrodynamics, the electric potential has infinitely many degrees of freedom. For any (possibly time-varying or space-varying) scalar field, 𝜓 , we can perform the following gauge transformation to find a new set of potentials that produce exactly the same electric and magnetic fields: V ′ = V − ∂ ψ ∂ t A ′ = A + ∇ ψ {\displaystyle {\begin{aligned}V^{\prime }&=V-{\frac {\partial \psi }{\partial t}}\\\mathbf {A} ^{\prime }&=\mathbf {A} +\nabla \psi \end{aligned}}} Given different choices of gauge,

1938-430: The electric potential (and all the equations used here) are in the forms required by SI units . In some other (less common) systems of units, such as CGS-Gaussian , many of these equations would be altered. When time-varying magnetic fields are present (which is true whenever there are time-varying electric fields and vice versa), it is not possible to describe the electric field simply as a scalar potential V because

1989-460: The electric potential could have quite different properties. In the Coulomb gauge , the electric potential is given by Poisson's equation ∇ 2 V = − ρ ε 0 {\displaystyle \nabla ^{2}V=-{\frac {\rho }{\varepsilon _{0}}}} just like in electrostatics. However, in the Lorenz gauge , the electric potential

2040-413: The electric potential, is only defined up to an additive constant: one must arbitrarily choose a position where the potential energy and the electric potential are zero. These equations cannot be used if ∇ × E ≠ 0 {\textstyle \nabla \times \mathbf {E} \neq \mathbf {0} } , i.e., in the case of a non-conservative electric field (caused by

2091-437: The energy of an electron is affected not only by the electric potential, but also by the specific atomic environment that it is in. When a voltmeter is connected between two different types of metal, it measures the potential difference corrected for the different atomic environments. The quantity measured by a voltmeter is called electrochemical potential or fermi level , while the pure unadjusted electric potential, V ,

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2142-414: The galvanic response advocated by Luigi Galvani , Alessandro Volta developed the so-called voltaic pile , a forerunner of the battery , which produced a steady electric current . Volta had determined that the most effective pair of dissimilar metals to produce electricity was zinc and silver . In 1861, Latimer Clark and Sir Charles Bright coined the name "volt" for the unit of resistance. By 1873,

2193-469: The human body by scientists including Bertrand Bajon and Ramón M. Termeyer  [ pl ] in the 1760s, and by John Walsh and Hugh Williamson in the 1770s. Alessandro Volta , a professor of experimental physics in the University of Pavia , was among the first scientists who repeated and checked Galvani’s experiments. At first, he embraced animal electricity. However, he started to doubt that

2244-499: The main defender of the theory of animal electricity. Galvani actively investigated animal electricity until the end of his life. The Cisalpine Republic , a French client state founded in 1797 after the French occupation of Northern Italy, required every university professor to swear loyalty to the new authority. Galvani, who disagreed with the social and political confusion, refused to swear loyalty, along with other colleagues. This led to

2295-483: The new authority depriving him of all his academic and public positions, which took every financial support away. Galvani died peacefully surrounded by his mother and father, in his brother’s house depressed and in poverty, on 4 December 1798. Galvani's legacy includes: Galvani, according to William Fox, was "by nature courageous and religious." Jean-Louis-Marc Alibert said of Galvani that he never ended his lessons “without exhorting his hearers and leading them back to

2346-399: The position of the object with respect to the field. Two such force fields are a gravitational field and an electric field (in the absence of time-varying magnetic fields). Such fields affect objects because of the intrinsic properties (e.g., mass or charge) and positions of the objects. An object may possess a property known as electric charge . Since an electric field exerts force on

2397-617: The potential of a continuous charge distribution ρ ( r ) becomes V E ( r ) = 1 4 π ε 0 ∫ R ρ ( r ′ ) | r − r ′ | d 3 r ′ , {\displaystyle V_{\mathbf {E} }(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\int _{R}{\frac {\rho (\mathbf {r} ')}{|\mathbf {r} -\mathbf {r} '|}}\mathrm {d} ^{3}r'\,,} where The equations given above for

2448-421: The surface. inside the sphere for uniform charge distribution. on the axis, where Q {\displaystyle Q} is the total charge uniformly distributed on the ring. Luigi Galvani Luigi Galvani ( / ɡ æ l ˈ v ɑː n i / , also US : / ɡ ɑː l -/ ; Italian: [luˈiːdʒi ɡalˈvaːni] ; Latin : Aloysius Galvanus ; 9 September 1737 – 4 December 1798)

2499-703: The system. This fact simplifies calculations significantly, because addition of potential (scalar) fields is much easier than addition of the electric (vector) fields. Specifically, the potential of a set of discrete point charges q i at points r i becomes V E ( r ) = 1 4 π ε 0 ∑ i = 1 n q i | r − r i | {\displaystyle V_{\mathbf {E} }(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}\sum _{i=1}^{n}{\frac {q_{i}}{|\mathbf {r} -\mathbf {r} _{i}|}}\,} where And

2550-474: Was an Italian physician, physicist, biologist and philosopher, who studied animal electricity . In 1780, using a frog, he discovered that the muscles of dead frogs' legs twitched when struck by an electrical spark. This was an early study of bioelectricity , following experiments by John Walsh and Hugh Williamson . Luigi Galvani was born to Domenico Galvani and Barbara Caterina Foschi, in Bologna , then part of

2601-444: Was defined in 1893 as 1 ⁄ 1.434 of the emf of a Clark cell . This definition was abandoned in 1908 in favor of a definition based on the international ohm and international ampere until the entire set of "reproducible units" was abandoned in 1948. A 2019 revision of the SI , including defining the value of the elementary charge , took effect on 20 May 2019. Electric potential Electric potential (also called

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