# Average electric field over a spherical surface

## Homework Statement

I was working out problem 4, chapter 3 of Introduction to Electrodynamics by Griffiths:

a) Show that the average electric field over a spherical surface, due to charges outside the sphere, is the same as the field at the centre.

b) What is the average due to charges inside the sphere?

## The Attempt at a Solution

I know the solution, but there are a few aspects I do not see:

Here you have the image Griffiths makes reference at:

Why $z^2 + r^2 - R^2 = z - Rcos \theta$ (law of cosines developement)?

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TSny
Homework Helper
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Why $z^2 + r^2 - R^2 = z - Rcos \theta$ (law of cosines developement)?
This equality is not correct. Instead, note the following substitution

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