Calculate amount of charge flow, when a conducting sphere of radius R and carrying a charge Q, is joined to an uncharged conducting sphere of radius 2R.

Options

A. `q/4`
B. `q/3`
C. `q/2`
D. `(2q)/3`

Answer

D

Explanation

Capacitance of first sphere `C_(1)=4piepsilon_(0)R`. Capacitance of second sphere `C_(2)=4pi epsilon_(0)(2R)=2C_(1)`, when they are in contact with the common potential difference between them
`V=q/(C_(1)+C_(2))`
Charge on `C_(2)=C_(2)V`
`=qC_(2)//C_(1)+C_(2)=2/3q`