Two combining spheres A and B of ra-dius a and b respectively are at the same potential. The ratio of the surface charge densities of A and B is ________.

Options

A. `b/a`
B. `a/b`
C. `a^2/b^2`
D. `b^2/a^2`

Answer

A

Explanation

Given electric potential of spheres are same i.e,
`V_A=V_B`
`1/(4 pi epsi_0).Q_1/a=1/(4 pi epsi_0).Q_2/b`
`Q_1/Q_2=a/b`..(i)
Surface charge density
`sigma=Q/(4 pi r^2)`
`implies sigma_1/sigma_2=Q_1/Q_2 times b^2/a^2`
`=a/b times b^2/a^2`
`=b/a`