Question

The electrostatic potential on the surface of a uniformly charged spherical shell of radius \( R = 10 \, \text{cm} \) is 120 V. The potential at the centre of the shell, at a distance 5 cm from the centre, and at a distance 15 cm from the centre of the shell are:

• A. \( 40 \, \text{V}, 40 \, \text{V}, 80 \, \text{V} \)
• B. \( 120 \, \text{V}, 120 \, \text{V}, 80 \, \text{V} \)
• C. \( 0 \, \text{V}, 120 \, \text{V}, 40 \, \text{V} \)
• D. \( 0 \, \text{V}, 0 \, \text{V}, 80 \, \text{V} \)

Hint:

For a spherical shell, the potential is constant at every point inside and on the shell, and it decreases as you move outside the shell.

Answer 1

The Correct Option is B

The potential due to a spherical shell is constant at all points outside the shell, and it is also constant at any point on the shell. The potential inside the shell is the same as at the surface. Therefore: - At the center of the shell, the potential is equal to the surface potential, which is 120 V. - At a distance 5 cm from the center, inside the shell, the potential is also 120 V, as the potential inside a spherical shell is constant. - At a distance 15 cm from the center, outside the shell, the potential is 80 V (due to the decrease in potential with distance from the shell). Thus, the correct answer is \( 120 \, \text{V}, 120 \, \text{V}, 80 \, \text{V} \).