Question

The electric potential in a certain region of space is given by $v=-3x^2+4x$, where x is in metres and v is in volts. In this region, the equipotential surfaces are

• A. Planes parallel to X-Z plane
• B. Planes parallel to X-Y plane
• C. Concentric cylinder with axis as X axis
• D. Concentric spheres centred at origin

Answer 1

The correct option is B. Planes parallel to Y-Z plane.

We know that,

$E=-\frac{\partial v}{dx}\hat{i}-\frac{\partial v}{dy}\hat{j}-\frac{\partial v}{dz}\hat{k}$

$E=(6x-4)\hat{i}$
So the EPS would be planes parallel to Y-Z plane, as E is perpendicular to EPS.