Problem 3.49

Find the potential $\varphi(x, y)$ of an electrostatic field $\mathbf{E}=$ $=2$ axy $\mathbf{i}+a\left(x^{2}-y^{2}\right) \mathbf{j},$ where $a$ is a constant, $\mathbf{i}$ and $\mathbf{j}$ are the unit vectors of the $x$ and $y$ axes.

\varphi=a y\left(\frac{y^{2}}{3}-x^{2}\right)+\text { const. }

Constant Electric Field in a Vacuum