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