JEE Main 2025 · 3 April · morning · Single correct · +4 / −1
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) 0 V, 120 V, 40 V
- (b) 120 V, 120 V, 80 V
- (c) 40 V, 40 V, 80 V
- (d) 0 V, 0 V, 80 V
Answer and solution
Answer (b) 120 V, 120 V, 80 V
Solution
Physics sir · 4 steps
Inside a charged shell the field is zero, so the potential does not change. It stays at the surface value.
- Inside the shell. The electric field inside a uniformly charged shell is zero. Potential changes only where there is a field, so every point inside, including the centre, has the same potential as the surface: 120 V.
- Outside the shell. Outside, the shell acts like a point charge Q at its centre. The potential therefore falls as 1/r.
V(r) = kQ/r ⇒ V(15 cm)/V(10 cm) = 10/15
- Put in numbers. V(15 cm) = 120 × 10/15 = 80 V.
- So. The potentials are 120 V at the centre, 120 V at 5 cm and 80 V at 15 cm. That is option (b).
The idea to keep. Zero field means constant potential, not zero potential. Inside a shell, V equals the surface value. Outside, V falls as 1/r, so scale the surface value by R/r.
Answer from the NTA final answer key. Solution by PrepWiser.