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Physics Question 39 – JEE-MAIN 2025

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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:

Recall the properties of electrostatic potential for a uniformly charged spherical shell both inside and outside its surface.

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Ninja Strategy•Constant Potential Inside

Recognize that the electrostatic potential inside a uniformly charged spherical shell is constant and equal to the potential on its surface, immediately eliminating options with 0V or other values for the center and r=5 cm.

Step 1: Identify Potential inside the shell✦ Active

For a uniformly charged spherical shell, the electric field inside the shell is zero. Consequently, the electrostatic potential inside the shell is constant and equal to the potential on its surface. Given R=10 cm and Vsurface=120 V.

Therefore, the potential at the centre (r=0) is Vcentre=120 V. The potential at r=5 cm (which is inside the shell, r<R) is Vr=5 cm=120 V.

Step 2: Calculate Potential outside the shell○ Expand

For points outside a uniformly charged spherical shell (r>R), the shell behaves like a point charge located at its center. The potential is given by Vout=kQr.

We know Vsurface=kQR=120 V. From this, kQ=Vsurface×R=120 V×10 cm.

For r=15 cm (outside the shell), Vr=15 cm=kQ15 cm=120 V×10 cm15 cm.

Step 3: Final Calculation and Result○ Expand

Calculating the potential at r=15 cm:

Vr=15 cm=120015 V=80 V

Thus, the potentials at the centre, r=5 cm, and r=15 cm are 120 V, 120 V, and 80 V respectively.

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