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

Medium

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Solution

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Correct option is C)

Electric field is directly propotional to $r$, therefore $E=kr$ We know that $V=−∫_{0}E.dr$ which gives $V=−2kr_{2} $ since V at $r=0$ is $0$ Hence V is proportional to $r_{2}$