Let k=(1)/(4πε0). Several charged…

Let k=(1)/(4πε0). Several charged bodies each carry total charge Q and have radius R. List-I names the point at which the electric potential (taken…

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Let

k=\dfrac{1}{4\pi\varepsilon_0}

. Several charged bodies each carry total charge

Q

and have radius

R

. List-I names the point at which the electric potential (taken zero at infinity) is evaluated; List-II gives the potential in units of

kQ/R

. Match List-I with List-II.

List-I
(P) Centre of a uniformly charged non-conducting solid sphere of radius

R

(Q) A point at distance

R/2

from the centre of that same solid sphere
(R) A point at distance

2R

from the centre of a thin conducting spherical shell of radius

R

(S) A point on the axis of a thin uniformly charged ring of radius

R

, at distance

R

from its centre

List-II
(1)

\dfrac12

(2)

1

(3)

\dfrac{11}{8}

(4)

\dfrac32

(5)

\dfrac{1}{\sqrt2}

Show answer and solution

Answer: (A) P→4, Q→3, R→1, S→5

Inside a uniformly charged solid sphere the potential is

V(r)=\dfrac{kQ(3R^2-r^2)}{2R^3}

. (P) At the centre,

V=\dfrac{3kQ}{2R}

, which is (4). (Q) At

r=R/2

V=\dfrac{kQ}{2R^3}\left(3R^2-\tfrac{R^2}{4}\right)=\dfrac{11kQ}{8R}

, which is (3). (R) Outside any spherically symmetric charge, the potential is

kQ/r

, so at

2R

it is

\dfrac{kQ}{2R}

, which is (1). (S) Every element of the ring is at distance

\sqrt{R^2+R^2}=\sqrt2R

from the point, so

V=\dfrac{kQ}{\sqrt2R}

, which is (5). Item (2),

kQ/R

, is the surface potential of the sphere and is not used. Thus P→4, Q→3, R→1, S→5.

Original question written in the JEE Advanced 2023 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