A solid conducting sphere of radius…

A solid conducting sphere of radius 1.0 cm carries charge +1 nC and sits at the centre of a concentric thick conducting spherical shell of inner…

One or more options correct

A solid conducting sphere of radius

1.0\ \mathrm{cm}

carries charge

+1\ \mathrm{nC}

and sits at the centre of a concentric thick conducting spherical shell of inner radius

2.0\ \mathrm{cm}

and outer radius

3.0\ \mathrm{cm}

. The shell carries a net charge

+2\ \mathrm{nC}

. Take

1/4\pi\varepsilon_0=9\times10^9\ \mathrm{N\,m^2C^{-2}}

and zero potential at infinity. Which of the following statements is/are correct?

A. The potential of the outer shell is $900\ \mathrm{V}$ .
B. The potential difference between the inner sphere and the shell is $450\ \mathrm{V}$ .
C. The potential of the inner sphere is $900\ \mathrm{V}$ .
D. If the shell is now earthed, the potential of the inner sphere becomes $450\ \mathrm{V}$ .

Show answer and solution

Answer: A, B, D

The inner sphere induces

-1\ \mathrm{nC}

on the inner surface of the shell, so the outer surface must hold

2-(-1)=+3\ \mathrm{nC}

. The shell's potential is that of this outer charge:

V_{shell}=9\times10^9\times3\times10^{-9}/0.03=900\ \mathrm{V}

, so (A) is true. The potential difference across the gap is

kq\left(\tfrac1a-\tfrac1b\right)=9\left(100-50\right)=450\ \mathrm{V}

, so (B) is true and the inner sphere is at

900+450=1350\ \mathrm{V}

, which makes (C) false. When the shell is earthed its outer surface charge leaves, the shell goes to

0\ \mathrm{V}

and the gap voltage is unchanged because the enclosed charge is still

+1\ \mathrm{nC}

; the inner sphere is therefore at

450\ \mathrm{V}

and (D) is true. Correct options: (A), (B), (D).

Original question written in the JEE Advanced 2019 Paper 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake