Electric field in a region is given by $\vec{E}=A x \hat{i}+B y \hat{j}$, where $A=10 \mathrm{~V} / \mathrm{m}^{2}$ and $B=5 \mathrm{~V} / \mathrm{m}^{2}$. If the electric potential at a point $(10,20)$ is 500 V , then the electric potential at origin is \_\_\_\_ V.

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Electrostatics

Electric field in a region is given by

E = A x \hat{i} + B y \hat{j}

, where

A = 10 V / m^{2}

and

B = 5 V / m^{2}

. If the electric potential at a point

(10, 20)

is 500 V , then the electric potential at origin is ____ V.

Answer: (C)

The potential follows from

V = - \int E \cdot d r

, giving

V (x, y) = - (\frac{A x ^{2}}{2} + \frac{B y ^{2}}{2}) + const

. Moving from the origin to

(10, 20)

V_{(10, 20)} - V_{0} = - \frac{A}{2} (10)^{2} - \frac{B}{2} (20)^{2} = - \frac{10}{2} (100) - \frac{5}{2} (400) = - 500 - 1000 = - 1500 V

. With

V_{(10, 20)} = 500 V

, the potential at the origin is

V_{0} = 500 + 1500 = 2000 V

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Single correct option