Electric field in a region is given by E = Axi + Byj, where A = 10 V/m² and B = 5 V/m². If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is ______ V. (a) 1000 (b) 0 (c) 2000 (d) 500

Electric field in a region is given by E = Axi + Byj, where A = 10… | JEE Main 2026 (22 Jan, Shift 1)

Q20JEE Main 2026 · 22 JAN · SHIFT 1Medium

Electric Potential & Equipotentials

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

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Answer: (c)

$V_O - V_P = -\int_P^O \vec{E}\cdot d\vec{r} = \left[\frac{Ax^2}{2} + \frac{By^2}{2}\right]_{O}^{P}$
$= \frac{10(10)^2}{2} + \frac{5(20)^2}{2} = 500 + 1000 = 1500\,\text{V}$
$V_O = 500 + 1500 = 2000\,\text{V}$
So the answer is (c) 2000.

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