# Potential energy of moving charge in field

## Homework Statement

1. Homework Statement [/B]

Prove the potential energy of interaction between an electric charge ##q## moving with velocity ##\vec{v}## and an electromagnetic field with potentials ##V## and ##\vec{A}## is given by ##U = qV-q \vec{v} \cdot \vec{A}##

## Homework Equations

Lorentz force ##\vec{F}=q(\vec{E}+\vec{v} \times \vec{B})##

##\vec{B} = \nabla \times \vec{A}##

##\vec{E} = -\nabla V - \frac{\partial \vec{A}}{\partial t}##

## The Attempt at a Solution

I don't really know how to begin this problem. I was thinking of using vector properties on the Lorentz force until I reach the desired property, since the force is the gradient of potential energy. Would that work?

Simon Bridge
Homework Helper
I don't really know how to begin this problem. I was thinking of using vector properties on the Lorentz force until I reach the desired property, since the force is the gradient of potential energy. Would that work?
Try it and see. (Note: how do you normally work out the potential energy function?)