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

Tardigrade Admin · Accepted Answer

Co-ordinates of the point =(x, y). Electric potential (V)=-K x y Distance of the point from origin (r)=√x2+y2 Ex =-( partial V/ partial x)=-( partial/ partial x)(-K x y)=K y Ey =-( partial V/ partial y)=-( partial/ partial y)(-K x y)=K x ∴ Er =√Ex2+Ey2 =√(K y)2+(K x)2=K r or Er propto r

Q. The electric potential at a point $(x, y)$ in the $x y$ -plane is given by $V = - K x y_{i}$ 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 xy -plane is given by V=−Kxyi​ The electric field intensity at a distance r from the origin varies as

r2

r

2 r

2r2

Co-ordinates of the point =(x,y). Electric potential (V)=−Kxy Distance of the point from origin (r)=x2+y2​ Ex​=−∂x∂V​=−∂x∂​(−Kxy)=Ky Ey​=−∂y∂V​=−∂y∂​(−Kxy)=Kx ∴Er​=Ex2​+Ey2​​ =(Ky)2+(Kx)2​=Kr or Er​∝r

Q. The electric potential at a point $(x, y)$ in the $x y$ -plane is given by $V = - K x y_{i}$ The electric field intensity at a distance $r$ from the origin varies as

$r^{2}$

$2 r^{2}$