Question

Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

• A. \[ (x + y)(y + z)(z + x) = \text{constant} \]
• B. \[ xyz = \text{constant} \]
• C. \[ xy + yz + zx = \text{constant} \]
• D. \[ (x^2 + y^2)(y^2 + z^2)(z^2 + x^2) = \text{constant} \]

Hint:

In electrostatics, equipotential surfaces are where the electric potential is constant, and they often involve simple relationships between the distances from the source charges.

Answer 1

The Correct Option is C

The potential generated by an infinitely long charged wire is directly proportional to the natural logarithm of the distance from the wire. To determine the equipotential surface, the potentials from three such wires are superimposed.
Step 1: The potential contribution from each individual wire is a function of its perpendicular distance.
Step 2: An equipotential surface is defined as the locus of points where the sum of the potentials from all three wires remains constant.
Step 3: Analysis of the resultant potential expressions reveals that the relationship \( xy + yz + zx = constant} \) accurately defines the equipotential surface.