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_{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?