Question

A thin spherical shell is charged by some source. The potential difference between the two points C and P (in V) shown in the figure is:
(Take \(\frac{1}{4}\pi\epsilon_0 = 9 × 109\)\(\frac{1}{4\pi\epsilon_0}=9\times10^9\) SI units)

• A. 3 × 10⁵
• B. 1 × 10⁵
• C. 0.5 × 10⁵
• D. Zero

Answer 1

The Correct Option is D

To ascertain the potential difference between points \( C \) and \( P \) on a charged thin spherical shell, we examine potential characteristics within and external to the shell. For a thin spherical shell:

• Within the shell (any location inside its radius), the electric potential remains constant. This stems from the electric field being zero inside the shell, a consequence of symmetry and Gauss's law. Consequently, the potential difference between any two internal points is zero.
• External to the shell, the shell acts as a point charge situated at its center. The potential \( V \) at a distance \( r \) from the center is calculated as \( V = \frac{kQ}{r} \), where \( Q \) represents the total charge on the shell and \( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \).
• If both points \( C \) and \( P \) are situated either inside the shell or at an identical radial distance from the center, the potential difference between them is zero.

Given that both points are located either within the shell or at the same radial distance, the potential difference is: Zero