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Potential energy of moving charge in field

  1. Apr 30, 2016 #1
    1. The problem statement, all variables and given/known data1. The problem statement, all variables and given/known data

    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}##

    2. Relevant 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}##

    3. 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?
     
  2. jcsd
  3. May 3, 2016 #2

    Simon Bridge

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    Try it and see. (Note: how do you normally work out the potential energy function?)
     
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