$(a)\;r^2\qquad(b)\;r\qquad(c)\;\large\frac{1}{r}\qquad(d)\;\large\frac{1}{r^2}$

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Answer : (b) r

Explanation :

$E_{x}=-\large\frac{\partial V}{\partial x}=ky$

$E_{y}=-\large\frac{\partial V}{\partial y}=kx$

$\overrightarrow{E}=E_{x} \hat{i} + E_{y} \hat{j}$

$\overrightarrow{E}=k_{y} \hat{i} +k_{x} \hat {j}$

$|\overrightarrow{E}|=\sqrt{k^2 y^2 + k^2 x^2}$

$|\overrightarrow{E}|= k\; \sqrt{x^2+y^2}$

$=k\;r$

Thus $\; |\overrightarrow{E}| \propto r $

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