Question

a conducting sphere A of radius a, with charge Q, is placed concentrically inside a conducting shell B of radius b. B is earthed. C is the common centre of A and B:

• A. The field at a distance r from C, where $a\le r\le b$, is $k\frac{Q}{r^2}$.
• B. The potential at a distance r from C, where $a\le r\le b$, is $k\frac{Q}{r}$.
• C. The potential difference between A and B is, $kQ(\frac{1}{a}-\frac{1}{b})$
• D. The potential difference between r and C, where $a\le r\le b$, is $kQ(\frac{1}{a}-\frac{1}{b})$

Answer 1

Answer: (A), (C), (D)

The correct options are
A The field at a distance r from C, where $a\le r\le b$, is $k\frac{Q}{r^2}$.
C The potential difference between A and B is, $kQ(\frac{1}{a}-\frac{1}{b})$
D The potential difference between r and C, where $a\le r\le b$, is $kQ(\frac{1}{a}-\frac{1}{b})$

This is spherical capacitance. -Q charge will appear on inner surface of outer sphere.
So the electric field in between the sphere is $E=k\frac{Q}{r^2}$
The potential difference between the sphere is $V=-{\int }_b^{a}Edr=-k{\int }_b^a\frac{Q}{r^2}dr=kQ(\frac{1}{a}-\frac{1}{b})$ where $a\le r\le b$