Function Conjunction → Functions composed of Physical Expressions
Functions for a point charge
The electric scalar potentialat due to a point charge at is:
The magnetic vector potentialat due to a point charge which had a velocity at is:
Functions for an ordered pair of point charges
A chargesubject to an electric scalar potential at due to a point charge at has an electric potential energy of:
A chargesubject 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 chargescan be derived from the scalar potential and the vector potential .
A chargewhich has a velocity of at will experience a Lorentz force due to a point charge at of:
The electric fieldis:
The magnetic fieldis:
The Lorentz Force can be expressed directly in terms of the potentials:
- = 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 chargeexperienced by a charge is:
The partial derivative of this with respect to timeis: