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

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KollegeApply · Accepted Answer

it is proportional to r2 Given: E \propto r and V = 0 at r =0 $\Rightarrow$ E = kr Also, E = - dV/dr \therefore V = - \int Edr \Rightarrow V = - \int krdr \Rightarrow V = - kr^$\frac{2}{2}$ + C Using the condition, V = 0 at r = 0, we get C =0. Therefore, V = - kr^$\frac{2}{2}$ \Rightarrow V \propto r^2

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