A conducting sphere of radius `R` and carrying a charge `Q` is joined to an uncharged conducting sphere of radius `2R`. The charge flowing between them will be

Options

A. `(1)/(4piepsilon_(0)).(Q^(2))/(4R)`
B. `(1)/(4pi epsilon_(0)).(Q^(2))/(2R)`
C. `(1)/(4pi epsilon_(0)).(Q^(2))/(R)`
D. `(2)/(2pi epsilon_(0)).(Q^(2))/(3R)`

Answer

A

Explanation

The capacitances of two are `C_(1)=4pi epsilon_(0)R` and `C_(2)=4pi epsilon_(0)(2R)`
`"Initial energy "=E_(i)=(Q^(2))/(2C_(1))`
Final energy `=E_(f)=(Q^(2))/(2C_(2))`
Heat produced `=E_(i)-E_(f)`
`=(Q^(2))/(2)[(1)/(4pi epsilon_(0)R)-(1)/(2xx4pi epsilon_(0)R)]`
`=(1)/(4pi epsilon_(0)).(Q^(2))/(2R)[1-(1)/(2)]`
`=(1)/(4pi epsilon_(0)).(Q^(2))/(4R)`