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The work per unit of charge is defined as the movement of negligible test charge between two points, and is expressed as the difference in electric potential at those points. The work can be done, for example, by generators , ( electrochemical cells ) or thermocouples generating an electromotive force .
The work done is given by the dot product of the two vectors, where the result is a scalar. When the force F is constant and the angle θ between the force and the displacement s is also constant, then the work done is given by: = If the force is variable, then work is given by the line integral:
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 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 change in electrostatic potential energy, U E, of a point charge q that has moved from the reference position r ref to position r in the presence of an electric field E is the negative of the work done by the electrostatic force to bring it from the reference position r ref to that position r.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
If the work for an applied force is independent of the path, then the work done by the force is evaluated from the start to the end of the trajectory of the point of application. This means that there is a function U ( x ), called a "potential", that can be evaluated at the two points x A and x B to obtain the work over any trajectory between ...
Considering the charge to be invariant of observer, the electric and magnetic fields of a uniformly moving point charge can hence be derived by the Lorentz transformation of the four force on the test charge in the charge's frame of reference given by Coulomb's law and attributing magnetic and electric fields by their definitions given by the ...
The Maxwell–Faraday equation (listed as one of Maxwell's equations) describes the fact that a spatially varying (and also possibly time-varying, depending on how a magnetic field varies in time) electric field always accompanies a time-varying magnetic field, while Faraday's law states that emf (electromagnetic work done on a unit charge when ...