Two conducting spheres of radii 3 cm and 1 cm are separated by a distance of 10 cm in free space. If the spheres are charged to same potential of 10 V each, then the force of repulsion between them is

Options

A. `((1)/(3)) xx 10^(-9) N`
B. `((2)/(9)) xx 10^(-9) N`
C. `((1)/(9)) xx 10^(-9) N`
D. `((4)/(3)) xx 10^(-9) N`

Answer

A

Explanation

`V_(1) = (1)/(4pi epsilon_(0))(Q_(1))/(R_(1)), 10 = (9 xx 10^(9) xx Q_(1))/(3 xx 10^(-2)), Q_(1) = (10^(-10))/(3)C`
`V_(2) = (1)/(4pi epsilon_(0))(Q_(2))/(R_(2)), 10 = (9 xx 10^(9) xx Q_(2))/(3 xx 10^(-2)), Q_(2) = (10^(-10))/(9)C`
`F = (1)/(4pi epsilon_(0))(Q_(1)Q_(2))/(r^(2)) = (9 xx 10^(9) xx 10^(-10) xx 10^(-10))/((0.1)^(2) xx 3 xx 9) = ((1)/(3)) xx 10^(-9) N`