A small conducting sphere of radius a mounted on an insulated handle and a positive charge q is inserted through a hole in the wall of a hollow conducting sphere of inner radius b and outer radius c. The hollow sphere is supported on an insulating stand and is initially uncharged. The small sphere is placed at the center of the hollow sphere. Neglect any effect of the hole. Which of the following statements will be true for this system?

Options

A. No work will be done in carrying a small charge from the inner conductor to the outer conductor.
B. The electric field at a point in the region between the spheres at a distance r from the center is equal to `q//4piepsilon_0r^2`.
C. The electric field at a point outside the hollow sphere at a distance r from the centre is `q//4piepsilon_0r^2`.
D. The potential of the inner sphere with respect to the outer sphere is given by `V_(ab) = q/(4piepsilon_0)(1/a-1/b)`.

Answer

B, C, D

Explanation

b.,c.,d.
Charge on inner sphere can be supposed to be concentrated as a point charge at the center, hence electric field at a point in the region between the spheres at a distance `r` from the center is `(q//4pi_(0)r^(2))`. Due to induction, equla and opposite charges will appear on the inner and outer surface of the outer sphere. Hence, net charge which can be supposed to be placed at the center is `q` and electric field due to it at a point outside the hollow sphere at a distance `r` from center is `(q//4piepsilon_(0)r^(2))`. Potential of inner sphre is `(q)/(4piepsilon_(0))((1)/(a)+(1)/(b)+(1)/(c))`
And potential of outer sphere is `(q)/(4piepsilon_(0)c)`
Potential of inner sphere with respect to the outer sphere `(q)/(4piepsilon_(0))((1)/(a)-(1)/(b))`