Question

An electric field $(-30 \hat{i}+20 \hat{j}) V m ^{-1}$ exists in space. If the potential at the origin is zero, then find the potential (in volt) at $(5\, m , 3\, m )$.

Answer 1

$d V =-\vec{E} \cdot d \vec{r}=-(-30 \hat{i}+20 \hat{j}) \cdot(d x \hat{i}+d y \hat{j}+d z \hat{k})$
$=30 d x-20 d y$
$\Rightarrow \int\limits_{0}^{V} d V=\int\limits_{(0,0)}^{(5,3)}(30 d x-20 d y)$
$\Rightarrow V=(30 x)_{0}^{5}-(20 y)_{0}^{3}$
$=150-60=90\, V$