Consider the following conclusions regarding the components of an electric field at a certain point in space given by ${\mathrm{E}}_{\mathrm{x}}=-\mathrm{Ky},{\mathrm{E}}_{\mathrm{y}}=\mathrm{Kx},{\mathrm{E}}_{\mathrm{z}}=0$.

Let us find Potential difference between any two points: 

$\begin{array}{l} {\mathrm{V}}_2-{\mathrm{V}}_1=-{\int }_{{\mathrm{x}}_1}^{{\mathrm{x}}_2} {\mathrm{E}}_{\mathrm{x}}\mathrm{dx}-{\int }_{{\mathrm{y}}_1}^{{\mathrm{y}}_2} {\mathrm{E}}_{\mathrm{y}}\mathrm{dy}\\ \Rightarrow {\mathrm{V}}_2-{\mathrm{V}}_1=+{\int }_{{\mathrm{x}}_1}^{{\mathrm{x}}_2} {\mathrm{K}}_{\mathrm{y}}\mathrm{dx}-{\int }_{{\mathrm{y}}_1}^{{\mathrm{y}}_2} {\mathrm{K}}_{\mathrm{x}}\mathrm{dy}\end{array}$

This can further be evaluated only if we know the dependance of x and y on each other or the path of integration. Hence field is nonconservative. To find the shape of lines of force:

$\begin{array}{l}\tan \mathrm{\theta }=\frac{{\mathrm{E}}_{\mathrm{y}}}{{\mathrm{E}}_{\mathrm{x}}}\text{ or }\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{{\mathrm{E}}_{\mathrm{y}}}{{\mathrm{E}}_{\mathrm{x}}}\\ \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{Kx}}{-\mathrm{Ky}}\text{ or }\mathrm{xdx}+\mathrm{ydy}=0\\ \frac{{\mathrm{x}}^2}{2}+\frac{{\mathrm{y}}^2}{2}=\mathrm{C}\text{ or }{\mathrm{x}}^2+{\mathrm{y}}^2=2\mathrm{C}\end{array}$

This is the equation of circle.