JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Electrostatics

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Consider the force F on a charge ' q ' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F , if ' q ' is placed at distance r from the centre of the shell?

(A) $F = \frac{1}{4 π ϵ _{0}} \frac{Qq}{R ^{2}}$ for $r < R$
(B) $\frac{1}{4 π ϵ _{0}} \frac{q Q}{R ^{2}} > F > 0$ for $r < R$
(C) $F = \frac{1}{4 π ϵ _{0}} \frac{Qq}{r ^{2}}$ for $r > R$ ✓ Correct
(D) $F = \frac{1}{4 π ϵ _{0}} \frac{Qq}{r ^{2}}$ for all $r$

Answer: (C)

Solution

A uniformly charged shell produces no field inside itself, so a charge placed at

r < R

feels

F = 0

. Outside the shell the whole charge

Q

acts as though concentrated at the centre, giving

F = \frac{1}{4 π ϵ _{0}} \frac{Qq}{r ^{2}}

for

r > R

, which at the surface reduces to

\frac{1}{4 π ϵ _{0}} \frac{Qq}{R ^{2}}

. The statement that holds is that for

r > R

the force is

F = \frac{1}{4 π ϵ _{0}} \frac{Qq}{r ^{2}}

JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Single correct option

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JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Electrostatics

Solution

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