JEE Main 2025 Apr 3 Shift 1, Physics Q14: Electric Potential

JEE Main2025Apr 3, Shift 1Physics

The electrostatic potential on the surface of uniformly charged spherical shell of radius $R = 10$ cm is 120 V. The potential at the centre of shell, at a distance $r = 5$ cm from centre, and at a distance $r = 15$ cm from the centre of the shell respectively, are :

A
120 V, 120 V, 80 V
B
40 V, 40 V, 80 V
C
0 V, 0 V, 80 V
D
0 V, 120 V, 40 V

Solution

For a uniformly charged thin spherical shell, the potential is constant throughout the interior (centre and all interior points), equal to the surface value:

$V_{centre} = V (r = 5 cm) = V_{surface} = 120 V .$

Outside the shell, $V (r) = \frac{k Q}{r}$ , and from the surface condition $\frac{k Q}{R} = 120 \Rightarrow k Q = 120 \times 0.10 = 12 V m .$

At $r = 15$ cm = 0.15 m: $V = \frac{12}{0.15} = 80 V .$

$∴$ Triple: 120 V, 120 V, 80 V.

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JEE Main 2025 Apr 3 Shift 1, Physics Q14: Electric Potential

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