Question

A spherical conductor `A` contains two spherical cavities as shown in Fig.2.127. The total charge on conductor itself is zero . However , there is a point charge `q_(1)` at the center of one cavity and `q_(2)` at the center of the other cavity . Another charge `q_(3)` is placed at a large distance `r` from the center of the spherical conductor.

The force acting on conductor `A` will be
A. zero
B. `(q_(3) (q_(1) + q_(2)))/(4 pi epsilon_(0) r^(2))`
C. `( - q_(3) (q_(1) + q_(2)))/(4 pi epsilon_(0) r^(2))`
D. `(q_(3) q_(1) + q_(2) q_(3) + q_(1) q_(2))/( 4 pi epsilon_(0) r^(2))`

Answer 1

Correct Answer - B
We see that that surface of two spherial cavities carries charges `q_(1), - q_(2)` respectively, and since the sphere A was not charged orginally, its sphereical surface must carry induced charges `(q_(1) + q_(2))`. Therefore, force acting on conductor A is `q_(3) (q_(1) + q_(2))//4 pi epsilon_(0) r^(2)`