In a region, the electric field is $(30 \bar{i}+40 \bar{j}) \mathrm{NC}^{-1}$. If the electric potential at…
In a region, the electric field is $(30 \bar{i}+40 \bar{j}) \mathrm{NC}^{-1}$. If the electric potential at the origin is zero, the electric potential at the point $(1 \mathrm{~m}, 2 \mathrm{~m})$ is
-60 V
-75 V
-55 V
-110 V
Solution
$\overrightarrow{\mathrm{E}}=(30 \hat{\mathrm{i}}+40 \hat{\mathrm{j}}) N \mathrm{NC}^{-1}, \mathrm{~V}(0,0)=0$
Now, $d v=-\vec{E} \cdot d \vec{r}=-(30 \hat{i}+40 \hat{j})(d x \hat{i}+d y \hat{j}+d z \hat{k})$
$\begin{aligned} & \Rightarrow \int_{(0,0)}^{(1,2)} \mathrm{dv}=-30 \int_0^1 \mathrm{dx}-40 \int_0^2 \mathrm{dy} \\ & \Rightarrow \mathrm{V}(1,2)-\mathrm{V}(0,0)=-30 \times 1-40 \times 2 \\ & \therefore \mathrm{~V}(1,2)=-110 \mathrm{~V}\end{aligned}$