Two concentric spherical conducting shells of radii 'a' and 2a are initially given charges +2Q and +Q respectively as shown. The total heat dissipated after switch 'S' has been closed is (where `k=(1)/(4piepsilon_(0))`)

Options

A. `(5kQ^(2))/(4a)`
B. `(kQ^(2))/(a)`
C. `(kQ^(2))/(2a)`
D. `(kQ^(2))/(4a)`

Answer

B

Explanation

`U_(i)=(k(2Q)^(2))/(2a)+(kQ^(2))/(4a)+(k(2Q)Q)/(2a)`
`=(2kQ^(2))/(a)+(5kQ^(2))/(4a)`
`U_(i)=(13kQ^(2))/(4a)`
`U_(f)=(k(3Q)^(2))/(4a)=(9kQ^(2))/(4a)`
`therefore` Total heat dissipated `DeltaH=U_(i)-U_(f)`
`=(13kQ^(2))/(4a)-(9kQ^(2))/(4a)`
`=(4kQ^(2))/(4a)=(kQ^(2))/(a)`