JEE Main 2026 — 22 January, Morning Shift — Question 40

$\overrightarrow{\mathrm{E}}=10 x \hat{\mathrm{i}}+5 y \hat{\mathrm{j}}$ $\mathrm{V}_{\text {at }(10,20)}=500 \mathrm{~V}$ $\Delta \mathrm{V}-\int \overrightarrow{\mathrm{E}} \cdot \mathrm{d} \overrightarrow{\mathrm{r}}$ $500-V_{0}=-\int_{(0,0)}^{(10,20)}(10 x \hat{i}+5 y \hat{j}) \cdot(d x \hat{i}+d y \hat{j})$ $500-V_{0}=-\left[5 x^{2}+\frac{5 y^{2}}{2}\right]_{(0,0)}^{(10,20)}$ $\mathrm{V}_{0}-500=\left(500+5 \times \frac{400}{2}\right)-(0-0)$ $\mathrm{V}_{0}-500=500+1000$ $\mathrm{V}_{0}=2000 \mathrm{~V}$