Problem 1.133

There are two stationary fields of force \(\mathbf{F}=a y \mathbf{i}\) and \(\mathbf{F}\) \(=a x \mathbf{i}+b y \mathbf{j},\) where \(\mathbf{i}\) and \(\mathbf{j}\) are the unit vectors of the \(x\) and \(y\) axes, and \(a\) and \(b\) are constants. Find out whether these fields are potential.