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A thin dielectric ring, radius R has a charge distribution (lambda) = acos^2(theta), where (theta) is...

A thin dielectric ring, radius R has a charge distribution (lambda) = acos^2(theta), where (theta) is the usual polar angle and "a" is a constant with units of charge/length. The ring lies centered in the x-y plane. Find the total charge Q on the ring and the potential at the center of the ring. Now suppose the ring has a uniform charge density such that the total charge is still Q. Find the potential at the center of the ring again. Does this hold for any z position (with x=y=0)?

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