Question

The electric potential at a point $\left(x , y\right)$ in the $x$ - $y$ plane is given by

$V=-Kxy$

The electric field intensity at a distance $r$ from the origin varies as

• A. $r^{2}$
• B. $r$
• C. $2r$
• D. $2r^{2}$

Answer 1

Answer: (B)

Co-ordinates of the point are (x, y)
Distance of point from origin,
$r=\sqrt{x^{2} + y^{2} ,} \, V=-kxy$
$E_{x}=-\frac{\partial V}{\partial x}=-\frac{\partial}{\partial x}\left(- k x y\right)=ky$
$E_{y}=-\frac{\partial V}{\partial y}=-\frac{\partial}{\partial y}\left(- k x y\right)=kx$
$ \, E=\sqrt{E_{x}^{2} + E_{y}^{2}}=k\sqrt{y^{2} + x^{2}}=kr$