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How to represent a time varying vector field

  1. Jan 8, 2015 #1
    1. The problem statement, all variables and given/known data
    I'm solving for the magnetic potential vector field given a time varying electrical field. It might seem silly, but I don't really understand how to approach the problem since the field varies on both space and time. I'm given the motion of a charged particle. Can someone explain how exactly I would represent the time varying electrical, electric potential, and magnetic potential fields. I'm not really having an issue with the Physics, it's the math.

    2. Relevant equations
    E(x,t)=-∇Φ-(∂A/∂t)


    3. The attempt at a solution
     
  2. jcsd
  3. Jan 9, 2015 #2

    BvU

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    Hello Vs, welcome to PF

    That is a bit of a generic question. Can be made as complicated as you want (relativistic ?). The issue is specifically adressed and worked out with the Lienard-Wiechert potential .

    From Ohio state:

    Differentiating the Lienard-Wiechert potentials for a moving point charge is,
    as the textbook says, straightforward but tedious". If you want to know
    the details, look in Jackson's Classical Electrodynamics, which specializes in
    straightforward tediousness.5

    5Sometimes, to be fair, it deviates into devious tediousness​

    My Jackson (2nd ed, 1975) Ch 6 is tedious, indeed. Pages look as clean as new, so I must have avoided them :)
    I would start with simple cases.
     
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