- #1

cwill53

- 220

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- Homework Statement
- Griffiths' Electrodynamics, 4th Edition, Problem 3.4

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

- Relevant Equations
- $$\mathbf{E}_{\textup{average}}=\frac{1}{4\pi R^2}\oint_{\textup{sphere}}^{}\mathbf{E}\, dS$$

The picture above shows the integral that needs to be evaluated, and the associated picture ## \cos\alpha ## can be obtained via the law of cosines. I'm simply confused as to where the ##\cos\alpha ## comes from in the first place. I just don't see why ##\cos\alpha ## is necessary in this expression.

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