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## Homework Statement:

- 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:

- This is where I'm stuck.

I'm sure the average is going to be an integral, but [itex]\displaystyle\frac{1}{4\pi R^2}\oint\mathbf{E}\cdot d\mathbf{a}[/itex] gives me a scalar, not a vector.