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## Homework Statement

A uniformly charged sphere (center O

_{1}) with radius a and charge +Q has an off-center cavity within it (center O

_{2}) with radius b. Show that the electric field within the cavity is uniform and is directed along the line of centers, according to the equation:

[tex]\vec{E} = \frac{Q}{4\pi\epsilon{o}(a^{3}-b^{3})}\vec{S}[/tex]

where [tex]\vec{S}[/tex] is the vector directed from O

_{1}to O

_{2}along the line of centers. HINT: Use the superposition principle.

## Homework Equations

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## The Attempt at a Solution

I was pretty stumped by this one. My biggest problem here is that the lack of symmetry makes it difficult to think of an appropriate equation/integrand. I thought about dividing the larger sphere along the radius of the smaller sphere to produce two equal hemispheres, but then I still wasn't sure how to find an appropriate integral, because the change in the radius isn't symmetric in any way. Gauss' law is out of the question/irrelevant, too. So where do I even begin?