A thick conducting spherical shell has…

A thick conducting spherical shell has inner radius 10 cm and outer radius 20 cm and carries a net charge of +3 nC. A point charge of +2 nC is held…

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A thick conducting spherical shell has inner radius

10\ \mathrm{cm}

and outer radius

20\ \mathrm{cm}

and carries a net charge of

+3\ \mathrm{nC}

. A point charge of

+2\ \mathrm{nC}

is held at its centre. Use

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

. Choose the correct statement(s).

A. The charge on the inner surface of the shell is $-2\ \mathrm{nC}$ .
B. The charge on the outer surface of the shell is $+3\ \mathrm{nC}$ .
C. The potential of the shell is $225\ \mathrm{V}$ .
D. If the shell is now earthed, the charge on its outer surface vanishes and the potential at a point $5\ \mathrm{cm}$ from the centre is $90\ \mathrm{V}$ .

Show answer and solution

Answer: A, C

Gauss's law inside the conductor requires zero field, so the inner surface carries

-q=-2\ \mathrm{nC}

; A is true. Conservation of charge then puts

3-(-2)=+5\ \mathrm{nC}

on the outer surface, not

+3\ \mathrm{nC}

; B is false. The outside field is that of a total charge

+5\ \mathrm{nC}

at the centre, so the shell potential is

9\times10^9\times5\times10^{-9}/0.20=225\ \mathrm{V}

; C is true. On earthing, the potential of the shell becomes zero, which removes the outer charge, leaving only

-2\ \mathrm{nC}

on the inner surface. At

r=5\ \mathrm{cm}

the potential is

kq\left(\dfrac1r-\dfrac1a\right)=9\times2\times(20-10)=180\ \mathrm{V}

, not

90\ \mathrm{V}

; D is false.

Original question written in the JEE Advanced 2016 Paper 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake