Two spherical cavities of radii `a` and `b` are hollowed out from the interior of a neutral conducting sphere of radius `R`. At the center of each cavity , a point charge is placed . Call these charges `q_(a)` and `q_(b)`.
The electric field at a distance `r` outside the conductor is

Options

A. `(1)/( 4 pi epsilon_(0)) (q_(b))/(r^(2))`
B. zero
C. `(1)/( 4 pi epsilon_(0)) ( q_(a) + q_(b))/( r^(2))`
D. `(1)/(4 pi epsilon_(0)) (q_(a))/(r^(2))`

Answer

C

Explanation

i. `sigma_(A) = ( - q_(a))/(4 pi a^(2)) , sigma_(B) = (-q_(b))/( 4 pi b^(2)) ,sigma_(R) = ( q_(a) + q_(b))/( 4 pi R^(2))`
ii. `E = (1)/( 4 pi epsilon_(0)) ( q_(a) + q_(b))/(r^(2)) ( Fig. S2.56)`
iii. `E_(a) = (1)/( 4 pi epsilon_(0)) (q_(a))/( r^(2))`