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

Math can be hard and physics can be even harder. But if that is your thing, continue on for more about Functions composed of Physical Expressions. For experts!

Or, if you want to the see the S.H.O. Drive Presentation, check it out here.

## Preface

Physics can be a challenging subject, especially in more difficult areas such as in quantum mechanics and string theory. However, the physics involved in classical electromagnetism is an intermediate level of difficulty. It's harder than Newtonian dynamics, but all of it exists in three dimensions of space + one dimension of time. No wormholes or hyper-dimensions here! Just classical electromagnetism. S.H.O. talk 17:09, 15 May 2016 (PDT)

## 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 from a charge at the position at is:

Using the product rule, the partial derivative of this with respect to time can be found. For example, the derivative of a product of two variables and with respect to time is:

.

Therefore, the partial derivative of the magnetic vector potential at due to with respect to time is:

 The partial derivative, with respect to time , of the proximity of the position of at time to the position of at the retarded time . According to an observer at time : the velocity a charge had at the retarded time , when it emitted a light signal which has now reached at position and time
 The proximity of the position of at time to the position of at the retarded time . According to an observer at time : the acceleration a charge had at the retarded time , when it emitted a light signal which has now reached at position and time