Question

The electric field in a region is directed outward and is proportional to the distance r from the origin. Taking the electric potential at the origin to be zero,

• A. it is uniform in the region
• B. it is proportional to r
• C. it is proportional to r${}^2$
• D. it increases as one goes away from the origion

Answer 1

Answer: (C)

it is proportional to r${}^2$

Electric field is directly propotional to $r$, therefore
$E=kr$
We know that
$V=-{\int }_0^r\overrightarrow{E.}\overrightarrow{dr}$
which gives
$V=-\frac{k{r}^2}{2}$ since V at $r=0$ is $0$
Hence V is proportional to $r^2$