Two conducting spheres of radii `5 cm` and `10 cm` are given a charge of `15mu F` each. After the two spheres are joined by a conducting wire, the charge on the smaller sphere is

Options

A. `20 muC`
B. `5muC`
C. `10 muC`
D. `15 muC`

Answer

C

Explanation

Common potential, `V = (Q_(1) + Q_(2))/(C_(1) + C_(2))`
`V = (Q_(1) + Q_(2))/(4pi epsilon_(0)r_(1) +4pi epsilon_(0)r_(2)) = (Q_(1) + Q_(2))/(4pi epsilon_(0)(r_(1) + r_(2)))`
`= (30 mu C)/(4pi epsilon_(0)(5 + 10) xx 10^(-2)) = (30 xx 10^(-6) xx 9 xx 10^(9))/(15 xx 10^(-2)) = 18 xx 10^(5) V`
Charge on smaller sphere, `Q._(1) = 4pi epsilon_(0)r_(1)V`
`= (1)/(9 xx 10^(9)) xx 5 xx 10^(-2) xx 18 xx 10^(5) = 10 xx 10^(-6) C = 10 muC`