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black_hole

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## Homework Statement

I am supposed to derive this equation: tan(phi) = γtan(θ) by performing an integration to find the flux of E through each of 2 spherical caps; the flux through each of these caps should be equal. The first cap spans the angle θ; the element of surface area may be taken as 2∏r^2sinθdθ and the field is constant and equal to the field of a stationary point charge. The second caps spans the angle phi, the field through which is described by E = (Q/4∏εr^2)((1-β^2)(1-β^2sin^2(phi))^(3/2) and the element of surface area is 2∏r^2sin(phi)d(phi). I've tried to do this integration but can't seem to get the end result right. If it helps this is from Purcell problems 5.11.

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