- #1

Maybe_Memorie

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## Homework Statement

I'd type this out but there's a bit too much formulae.

http://www.maths.tcd.ie/~tristan/MA3431/Homework_1.pdf

It's problem 2. I'm just wondering if my solution is correct.

Thanks in advance!

## Homework Equations

## The Attempt at a Solution

In this problem I'm taking R

_{o}= |x

_{o}- x'|

The volume in question is charge-free so the charge density, ρ(x'), is zero so the first term on the right hand side of the potential vanishes.

Also, ∂/∂n(1/R

_{o}) = -1/R

^{2}

_{o}

Substituting this into the potential function gives the required result.

For the second part of 2 we use the divergence theorem (which I won't state here due to my lack of latex skills) as told.

We know that ∂[itex]\Phi[/itex]/∂n = ∇[itex]\Phi[/itex].n and from the definition of the electric field E we end up with -E.n.

When this is used in the divergence theorem we end up with the volume integral of ∇.E which is equal to ρ/ε which vanishes in a charge free volume.

We now have the required expression.

(Haven't gotten to part 3 yet, will be posted soon.)

I know I haven't explained everything in a great way, but it's a lot easier on paper than it is online to write out loads of partials and surface integrals.