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  4. An electric field vecE=(25 hati+30 hatj)NC-1 exists in a region of space. If the potential at the origin is taken to be zero then the potential at x = 2 m, y = 2 m is ;

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Q. An electric field $\vec{E}=\left(25 \hat{i}+30 \hat{j}\right)NC^{-1}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at $x = 2\, m$, $y = 2\, m$ is ;

JEE MainJEE Main 2015Electrostatic Potential and Capacitance

Solution:

$\Delta V=-\int_\limits{A}^{B} \vec{E} \cdot d \bar{r}$
$=-\int(25 i+30 j) \cdot(dxi +dyj)$
$\Rightarrow V_{B}-V_{A}=-\int 25 d x+30 d y$
$\Rightarrow V_{B}=-25(x)_{0}^{2}-30(y)_{0}^{2}=-50-60=-110\, V$