Average electric field over a spherical surface

[alexmahone]

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 \displaystyle\frac{1}{4\pi R^2}\oint\mathbf{E}\cdot d\mathbf{a} gives me a scalar, not a vector.

 

[alexmahone]

It appears that my question has already been asked and answered here: https://www.physicsforums.com/threads/average-electric-field-over-a-spherical-surface.966561/

Sorry.