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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.

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

#### 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.

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