Two spherical conductors A and B of radii 1mm and 2mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres A and B is

Options

A. `1:2`
B. `2:1`
C. `1:4`
D. `4:1`

Answer

B

Explanation

Here, `r_(1) = 1mm, r_(2) = 2mm, d = 5mm`
When spheres are connected by a conducting wire, charge flows from the sphere at higher potential to the sphere at lower potential, till their potential become equal.
Now `(C_(1))/(C_(2)) = (r_(1))/(r_(2)) = (1)/(2)`
As potential V is same, therefore
`(q_(1))/(q_(2)) = (C_(1)V)/(C_(2)V) = (C_(1))/(C_(2)) = (1)/(2)`
Now `(E_(1))/(E_(2)) = ((1)/(4pi epsilon_(0))(q_(1))/(r_(1)^(2)))/((1)/(4pii epsilon_(0))(q_(2))/(r_(2)^(2))) = (q_(1))/(q_(2)) xx ((r_(2))/(r_(1)))^(2) = (1)/(2)((2)/(1))^(2) = 2`