A uniformly charged sphere (center 0,0) with radius 2a and volume charge density [tex]\sigma[/tex] has a cavity within it (center 0,a) with radius a. Show that the electric field within the cavity is uniform and E(adsbygoogle = window.adsbygoogle || []).push({}); _{x}=0 E_{y}=[tex]\frac{a\sigma}{3\epsilon}[/tex] where \epsilon is the permittivity of free space.

Hi, I am able to prove the E field however I don't understand why we are only concern of the x and y-axis what about the z-axis? Why is E=E_{y}? Why is the E field of the cavity solely due to the y-axis? If that is the case won't the answer be the same if the question ask for a circle instead of a sphere?

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# Homework Help: Electric field inside a cavity within a uniformly charged sphere

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