Explore BrainMass

Explore BrainMass

    Electrostatic Field and Potential

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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
    https://brainmass.com/physics/gauss-law/electrostatic-field-potential-38895

    Attachments

    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.

    $2.49

    ADVERTISEMENT