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In the circuit shown in figure...

In the circuit shown in figure

Text Solution

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Self energy is equal to interaction energy of charges constituting the thick spherical shell.
Consider core of outer radius r having charge q, layer of infinitesimal thickness dr with charge dq.
Since core can be assumed to be a point charge at the centre wtih `q=p.(4)/(3)pi(r^(3)-R^(3))`
`therefore` Electrostatic interaction energy of point charge and the layer is given by
`dU=(1)/(4piepsilon_(0))(q.dq)/(r)=(1)/(4piepsilon_(0))=(rho(4)/(3)pi(r^(3)-R^(3)).rho4pir^(2)dr)/(r)`
`U=underset(R)overset(2R)int(rho^(2)4pi)/(3epsilon_(0))(r^(4)-R^(3)r)dr`
`U=(rho^(2)4pi)/(3epsilon_(0))[(r^(5))/(5)-(R^(3)r^(2))/(2)]_(R)^(2R)=(94)/(15)(rho^(2)piR^(5))/(epsilon_(0))`
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