Two spherical conductors of radii `R_1 and R_2` are separated by a distance much larger than the radius of eighter sphere. The spheres are connected by a conducting wire as shown in (Fig. 3.128). If the charges on the spheres in equilibrium are `q_1 and q_2`, respectively, what is the ratio of the field strength at the surfaces of the spheres ?
.

Options

A. `R_2//R_1`
B. `R_2^2//R_1^2`
C. `R_1//R_2`
D. `R_1^2//R_2^2`

Answer

a

Explanation

Their potential will be same, i.e., `V_1 = V_2`
or `(kq_1)/R_(1) = (kq_2)/R_(2)` or `q_(1)/q_(2) = R_(1)/R_(1)`
or `(E_1)/(E_2) = (kq_1//R_1^2)/(kq_2//R_2^2) = q_(1)/q_(2)(R_(2)/R_(1))^2`
=`R_(1)/R_(1) (R_(2)/R_(1))^2 = R_(2)/R_(1)`.