- #1
mr.hood
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Homework Statement
A uniformly charged sphere (center O1) with radius a and charge +Q has an off-center cavity within it (center O2) 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 O1 to O2 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?