The electric potential at a point (x , y) in the x - y plane is given by V=-Kxy The electric field intensity at a distance r from the origin varies as

Question

The electric potential at a point (x , y) in the x - y plane is given by V=-Kxy The electric field intensity at a distance r from the origin varies as (A) r2 (B) r (C) 2r (D) 2r2

Tardigrade Admin · Accepted Answer

Co-ordinates of the point are (x, y)
Distance of point from origin,

r = x^{2} + y^{2}, V = - k x y

E_{x} = - \frac{\partial V}{\partial x} = - \frac{\partial}{\partial x} (- k x y) = k y

E_{y} = - \frac{\partial V}{\partial y} = - \frac{\partial}{\partial y} (- k x y) = k x

E = E_{x}^{2} + E_{y}^{2} = k y^{2} + x^{2} = k r

Q. The electric potential at a point $(x, y)$ in the $x$ - $y$ plane is given by

$V = - K x y$

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

$r^{2}$

$r$

$2 r$

$2 r^{2}$

Q. The electric potential at a point (x,y) in the x - y plane is given by V=−Kxy The electric field intensity at a distance r from the origin varies as

r2

r

2r

2r2

Co-ordinates of the point are (x, y) Distance of point from origin, r=x2+y2,​V=−kxy Ex​=−∂x∂V​=−∂x∂​(−kxy)=ky Ey​=−∂y∂V​=−∂y∂​(−kxy)=kx E=Ex2​+Ey2​​=ky2+x2​=kr

Q. The electric potential at a point $(x, y)$ in the $x$ - $y$ plane is given by

$V = - K x y$

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

$r^{2}$

$r$

$2 r$

$2 r^{2}$