Question

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. $\frac{1}{r^2}$

Answer 1

The correct option is B r

$E_x=-\frac{dV}{dx}=-ky;E_y=-\frac{dV}{dy}=-kx$

$E=\sqrt{E_x^2+E_y^2}=k\sqrt{x^2+y^2}=kr\Rightarrow E\infty r$