Consider the following conclusiond regarding the components of an electric field at a certain point in space given by `E_x = -Ky, E_y = Kx, E_z = 0` .

Options

A. The field is conservative.
B. The field is nonconservative.
C. The lines of force are straight lines.
D. The lines of force are circles.

Answer

B, D

Explanation

b.,d.
Let us find potential difference between any two points:
`V_(2)-V_(1)=-underset(x_(1))overset(x_(2))intE_(x)dx-underset(y_(1))overset(y_(2))intE_(y)dy`
`rArr V_(1)-V_(1)=+underset(x_(1))overset(x_(2))intK_(y)dx-underset(y_(1))overset(y_(2))intK_(x)dy`
This can further be evaluated only if we know the dependance of `x` and `y` on each other or the path of intergration. Hence field is nonconservative. To find the shape of lines of force:
`tantheta=(E_(y))/(E_(x))` or `(dy)/(dx)=(E_(y))/(E_(x))`
or `(dy)/(dx)=(K_(x))/(-K_(y))` or `xds+ydy=0`
or `(x^(2))/(2)+(Y^(2))/(2)=C` or `x^(2)+y^(2)=2C`
This is the equation of circle.