The electric potential at a point $(x,\;y)$ in the $x - y$ plane is given by $V = - kxy$. The field intensity at a distance $r$ from the origin varies as
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(b) ${E_x} = - \frac{{dV}}{{dx}} = - \,ky$; ${E_y} = - \frac{{dV}}{{dy}} = \, - kx$
$E = \sqrt {E_x^2 + E_y^2} = k\sqrt {{x^2} + {y^2}} = kr$=
$E = \sqrt {E_x^2 + E_y^2} = k\sqrt {{x^2} + {y^2}} = kr$=
$E \propto r$
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