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    Electrostatic Field and Potential

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    I would appreciate help in completing the proof of the equation on the
    second line of the attached file.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:17 pm ad1c9bdddf


    Solution Preview

    What you need to prove is not that div[phi E] = 0, but rather that div[phi E] integrated over a volume approaches zero in the limit that the volume becomes infinitely large. If div[phi E] were a positive definite quantity then this would also imply that div[phi E] = 0 everywhere, but it isn't! div[phi E] can be negative or positive.

    I'm now going to derive the result step by step.

    Consider the volume integral:

    Volume integral [rho phi].

    Replacing rho = epsilon_0 div E ...

    Solution Summary

    The electrostatic field and potentials are determined. A detailed solution is given.