Question

An electric field $\overrightarrow{E}=(\overrightarrow{i}20+\overrightarrow{j}30)N{C}^{-1}$ exists in the space. If the potential at the origin is taken to be zero, find the potential at $(2m,2m)$.

Answer 1

The electric field in the region is given by: $E=(\hat{i}20+\hat{j}30)N/C$

The position of the point is at $(2m,2m)$

The displacement vcector for the point is $r=(2i+2j)$

Therefore, the potential at the point is:

So, $V=-\overrightarrow{E}\times \overrightarrow{r}$

$=-(i20+30J)(2\hat{i}+2j)$

$=-(2\times 20+2\times 30)=-100V$.