Two concentric thin conducting sphereical shells having radii `R` and `2R` are as shown in the figure .A charge `+Q` is given to the shell `A` and `-4Q` is given to the shell `B` .If `A` and `B` are connected by a thin conducting wire then the amount of heat produced after the connection is

Options

A. `(3Q^(2))/(4piepsilon_(0)R)`
B. `(Q^(2))/(16piepsilon_(0)R)`
C. `(5q^(2))/(8piepsilon_(0)R)`
D. `(Q^(2))/(8piepsilon_(0)R)`

Answer

B

Explanation

`U_(i)=(Q^(2))/(8piepsilon_(0)R)+(16Q^(2))/(16piepsilon_(0)R)-(1)/(4piepsilon_(0))(4Q^(2))/(2R)`
` =(2Q^(2)-16Q^(2)-8Q^(2))/(16piepsilon_(0)R)=(5Q^(2))/(8piepsilon_(0)R)`
`U_(f)=(9Q^(2))/(16piepsilon_(0)R)`
Heat pr oduced =`(5Q^(2))/(8piepsilon_(0)R)-(9Q^(2))/(16piepsilon_(0)R)`
`Q^(2)//16piepsilon_(0)R`