Average electric field over a spherical surface

Thread starter alexmahone
Start date May 14, 2019
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Average Electric Electric field Field Spherical Surface

May 14, 2019

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.

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May 14, 2019

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.

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