JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Electrostatics

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Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance

(r)

from the centre?

(A)(see structure)
(B)(see structure)
(C)(see structure)
✓ Correct
(D)(see structure)

Answer: (C)

Solution

Inside a charged conducting sphere the field is zero, so no work is needed to move a charge and the potential stays constant at its surface value

\frac{k Q}{R}

right up to

r = R

. Outside the sphere the charge behaves as if concentrated at the centre, giving

V = \frac{k Q}{r}

, which falls off hyperbolically with distance and joins the constant inner value continuously at the surface. The variation that is flat for

r < R

and then decreases as

1/ r

for

r > R

represents this behaviour.

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Single correct option

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