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Find the electric potential energy of a uniformly charged sphere.

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Potential due to ring element of radius r and
thickness dr is `dV=underset(0)overset(R)int(1)/(4piepsilon_(0))(sigma(2pirdr))/(sqrt(r^(2)+x^(2)))`
`implies V=(2sigma)/(4piepsilon_(0))[sqrt(r^(2)+x^(2))]_(0)^(R)=(sigma)/(2epsilon_(0))(sqrt(R^(2)+x^(2))-x)`
`E=-(dV)/(dx)=(sigma)/(2epsilon_(0))((2x)/(2sqrt(R^(2)+x^(2)))-1)=(sigma)/(2epsilon_(0))(1-(x)/(sqrt(R^(2)+x^(2))))`
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