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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

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Solution

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Correct option is C)

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

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