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In a solid uniformly charged sphere of t...

In a solid uniformly charged sphere of total charge Q and radius R, if energy stored out side the sphere is `U_(0)` joules then find out self energy of sphere in term of `U_(0)` ?

Text Solution

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For `x gt R ,E (x) = (1)/( 4pi epsilon_(0)). (Q)/(x^(2))`
`:. U _(OUT) = int dU = int_(x=R)^(x= infty)(1)/(2) epsilon_(0) E_((x))^(2) xx 4 pi x^(2) dx = (Q^(2))/(8 pi epsilon_(0)R)`
`U_("TOTAL") = U _(IN)+U_(OUT) = (1)/(5) (Q^(2))/( 8 pi epsilon_(0)R)+ ( Q^(2))/( 8 pi epsilon_(0)R) = ( 6)/( 5) ( Q^(2)) /( 8 pi epsilon_(0)R) = (3)/(5) . (Q^(2))/( 4pi epsilon_(0)R)`
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