A solid conducting sphere of radius…

A solid conducting sphere of radius a=10 cm carries a charge +Q and is placed concentrically inside a thick, initially uncharged, conducting…

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A solid conducting sphere of radius

a=10\ \mathrm{cm}

carries a charge

+Q

and is placed concentrically inside a thick, initially uncharged, conducting spherical shell of inner radius

b=20\ \mathrm{cm}

and outer radius

c=30\ \mathrm{cm}

. Let

k=1/4\pi\varepsilon_0

and take the potential at infinity as zero. Which of the following statement(s) is(are) correct?

A. The charge on the outer surface of the shell is $+Q$ .
B. The potential of the inner sphere is $10\,kQ\ \mathrm{m^{-1}}$ .
C. If the outer surface of the shell is then connected to earth, the potential of the inner sphere becomes $5\,kQ\ \mathrm{m^{-1}}$ .
D. The electric field at a point $25\ \mathrm{cm}$ from the centre equals $kQ/(0.25\ \mathrm{m})^2$ , directed radially outward.

Show answer and solution

Answer: A, C

Charge

+Q

on the inner sphere induces

-Q

on the inner surface of the shell, so the neutral shell carries

+Q

on its outer surface and (A) is correct. The potential of the inner sphere is

V=kQ\left(\dfrac1a-\dfrac1b+\dfrac1c\right)=kQ\,(10-5+3.33)\ \mathrm{m^{-1}}=8.33\,kQ\ \mathrm{m^{-1}}

, not

10\,kQ\ \mathrm{m^{-1}}

(which ignores the shell), so (B) is wrong. If the outer surface is earthed, the shell is at zero potential and its outer charge flows away, leaving

-Q

on the inner surface only; then

V=kQ\left(\tfrac1a-\tfrac1b\right)=5\,kQ\ \mathrm{m^{-1}}

and (C) is correct. At

r=25

cm the point lies inside the conducting material of the shell, where the field is zero, so (D) is wrong. Answer: A, C.

Original question written in the JEE Advanced 2019 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