Q. 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
A) $r^{2}$
B) $r$
C) $\frac{1}{r}$
D) $\frac{1}{r^{2}}$
Explanation
(b) $E_{x} = - \frac{dV}{dx} = + ky\ ;E_{y} = - \frac{dV}{dy} = + kx$
$\Rightarrow E = \sqrt{E_{x}^{2} + E_{y}^{2}} = k\sqrt{x^{2} + y^{2}} = kr \Rightarrow E \propto r$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.