# Difference between revisions of "Functions composed of Physical Expressions"

## Functions for a point charge

The electric scalar potential at due to a point charge at is:

The magnetic vector potential at due to a point charge which had a velocity at is:

## Functions for an ordered pair of point charges

A charge subject to an electric scalar potential at due to a point charge at has an electric potential energy of:

A charge subject to a magnetic vector potential at due to a point charge which had a velocity at has a potential momentum of:

### Lorentz Force for

The Lorentz Force between charges can be derived from the scalar potential and the vector potential .

A charge which has a velocity of at will experience a Lorentz force due to a point charge at of:

The electric field is:

The magnetic field is:

The Lorentz Force can be expressed directly in terms of the potentials:

Where:

• = negative the gradient of the scalar potential .
• = negative the partial derivative of the magnetic vector potential with respect to time .
• = the cross product of the velocity of the charge and the curl of the magnetic vector potential due to charge .

To restate from a previous section, the magnetic vector potential of a charge experienced by a charge is:

The partial derivative of this with respect to time is:

Where:

• = the acceleration of at the retarded time according to an observer at time sharing the same inertial frame as .

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