For the situation shown in the figure below (assume ` r gtgt` length fo dispole ) mark out the correct statement (s) -
.

Options

A. Potential of the conductor is `(q)/(4 pi varepsilon_(0) (d+R))`
B. Potential of the conductor is `(q)/(4 pi varepsilon_(0) d)`
C. Potential of the conductor can't be determined as nature of distribution of induced charges is not known
D. Potential at point B due to induced charges is `(-1R)/(4 pi varepsilon_(0) (d+R)d)`

Answer

A, D

Explanation

(A) Potential of the conductor will be equal to potential at centre of sphere due to charge `q`
`V= 1/( 4 pi in_0) q/( (d +R))`
(D) `vec E_q + vec E _(q ("induced")) = 0` inside conductor
`vec E_(q ("induced ")) =- vec E_q = (Kq)/x^2 ` towards `q`
` int_0^(V_B) dV =- int _((R +d))^d vec E. d vec x rArr V_B int_((R_d))^d Edx`
` V_B = int _(R +d) (Kq)/c^2 dx rArr V_B = (-qR)/(4 pi int _0 (d+R))`.