Electric field in a region is given by where and . If the electric potential at a point (10, 20) is 500 V, then the electric potential at the origin is ________ V. [2026]

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Solution

Q.
Electric field in a region is given by $\vec{E} = A x \hat{i} + B y \hat{j},$ 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 the origin is ________ V. [2026]

1 1000

2 0

3 500

4 2000

Ans.
(4)

$\vec{E} = 10 x \hat{i} + 5 y \hat{j}$

$V_{at (10, 20)} = 500 V$

$Δ V = - \int \vec{E} \cdot d \vec{r}$

$500 - V_{0} = - \int_{(0, 0)}^{(10, 20)} (10 x \hat{i} + 5 y \hat{j}) \cdot (d x \hat{i} + d y \hat{j})$

$500 - V_{0} = - {[5 x^{2} + \frac{5 y^{2}}{2}]}_{(0, 0)}^{(10, 20)}$

$V_{0} - 500 = (500 + 5 \times \frac{400}{2}) - (0 - 0)$

$V_{0} - 500 = 500 + 1000$

$V_{0} = 2000 V$

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