Question

Consider a group of charges \( q_1, q_2, q_3, \ldots \) such that \( \sum q \neq 0 \). Then equipotentials at a large distance, due to this group are approximately:

• A. Plane
• B. Spherical surface
• C. Paraboloidal surface
• D. Ellipsoidal surface

Hint:

When dealing with the potential due to multiple point charges at large distances, you can often simplify the calculation by treating them as a single point charge whose magnitude is the sum of the individual charges.

Answer 1

The Correct Option is B

Analyzing the influence of multiple point charges at a distance. At large distances, the individual effects of point charges \( q_1, q_2, q_3 \) on the potential can be considered to merge into a single effect similar to that of a single point charge with their cumulative charge. Therefore, the potential \( V \) at a point in space due to these charges resembles that from a single equivalent charge.
Considering the shape of equipotentials. The equipotential surfaces of a single point charge are spherical. Since at large distances the group of charges behaves like a single point charge, the equipotential surfaces thus formed will also be spherical.