Two metallic spheres of radii 1 cm and 3 cm are given charges of `-1 xx 10^(-2) C ` and `5 xx 10^(-2) C` , respectively . If these are connected by a conducting wire , the final charge on the bigger sphere is

Options

A. `2 xx 10^(-2)C`
B. `3 xx 10^(-2)C`
C. `4 xx 10^(-2)C`
D. `1 xx 10^(-2)C`

Answer

B

Explanation

When the given metallic speres are connected by a conducting wire, charge will flow till both the spheres acquire a common potential which is given by
Common potential,
`V = (q_(1) + q_(2))/(C_(1) + C_(2)) = (-1 xx 10^(-2) + 5 xx 10^(-2))/(4pi epsilon_(0)R_(1) + 4pi epsilon_(0)R_(2))`
`= (4 xx 10^(-2))/(4pi epsilon_(0)(1 xx 10^(-2) + 3 xx 10^(-2))) = (4 xx 10^(-2))/(4pi epsilon_(0) xx 4 xx 10^(-2))` ...(i)
`:.` Final charge on the bigger sphere is
`q._(2) = C_(2)V = 4pi epsilon_(0)R_(2)V`
`= 4pi epsilon_(0) xx 3 xx 10^(-2) xx (4 xx 10^(-2))/(4pi epsilon_(0) xx 4 xx 10^(-2))` (Using (i))
`= 3 xx 10^(-2)C`