The potential in an electric field varles as `v= (x^(2) -y^(2))` . The electric lines of the force in `x-y` plane are

Options

A.
B.
C.
D.

Answer

C

Explanation

The potential in an electric field varies as
`:. ` Electric field
`B=- [(dv)/(dx) hat(I ) + (dv)/(dy ) hat(j )]`
`=- [(d )/( dx) (x^(2) -y^(2)) hat(i) + (d )/(dy ) (x^(2)-y^(2)) hat(j ) ]`
`E = - [2x hat(j ) - 2 y hat(j ) ] rArr E=- 2x hat(j) + 2y hat(i)]`
Expression of the electric field is linear equation in two variables i.e., straight lines x-y plane and slope having `45^(@), 35^(@)` etc ` Hence the option (c ) represent correct graph.