Question

Two stationary point particles with equal and opposite charges are at some fixed distance from each other. The points having zero electric potential lie on:

• A. A sphere
• B. A plane
• C. A cylinder
• D. Two parallel planes

Hint:

For a dipole, equipotential surfaces near the midpoint are approximately cylindrical in shape.

Answer 1

The Correct Option is B

The problem involves two stationary point particles with equal and opposite charges placed at a fixed distance from each other. We are tasked with identifying the geometric shape on which the points of zero electric potential lie.

To solve this, let's first understand the concept of electric potential:

1. **Electric Potential Due to a Point Charge:** The electric potential \(V\) at a distance \(r\) from a point charge \(Q\) is given by the formula:

\(V = \frac{kQ}{r}\)

where \(k\) is Coulomb's constant.

2. **Superposition Principle:** When there are multiple charges, the total electric potential at a point is the algebraic sum of the potentials due to each charge separately.

For two charges \(+Q\) and \(-Q\), the potentials add up algebraically:

\(V_{\text{total}} = V_{+Q} + V_{-Q} = \frac{k(+Q)}{r_1} + \frac{k(-Q)}{r_2}\)

3. **Zero Electric Potential:** At the locations where these two potentials cancel each other out, the total electric potential is zero:

\(\frac{k(+Q)}{r_1} = \frac{k(-Q)}{r_2}\)

Rearranging gives:

\(\frac{1}{r_1} = \frac{1}{r_2}\)

4. **Geometrical Implication:** The condition \(r_1 = r_2\) describes the locus of points equidistant from both charges. This geometrical locus is a plane perpendicular to the line joining the two charges and passing through the midpoint.

Therefore, the correct answer is that the points of zero potential lie on a plane.