Electric Potential & Equipotentials question from JEE Main 2025 (28 Jan, Shift 1)

Answer: (a)

1. Potential of a line charge: $V = -\frac{\lambda}{2\pi\varepsilon_0}\ln d + C$, $d$ = distance from the line.
2. Distances from x, y, z axes: $\sqrt{y^2 + z^2}$, $\sqrt{z^2 + x^2}$, $\sqrt{x^2 + y^2}$.
3. $V = -\frac{\lambda}{4\pi\varepsilon_0}\ln\left[(x^2 + y^2)(y^2 + z^2)(z^2 + x^2)\right] + C'$
4. $V$ constant $\Rightarrow (x^2 + y^2)(y^2 + z^2)(z^2 + x^2) =$ constant. So the answer is (a).