All Problems Constant Electric Field in a Vacuum
Problem 3.36
Determine the electric field strength vector if the potential of this field depends on \(x, y\) coordinates as a) \(\varphi=a\left(x^{2}-y^{2}\right)\) (b) \(\varphi=a x y\) where \(a\) is a constant. Draw the approximate shape of these fields using lines of force (in the \(x, y\) plane).
3.36. (a) \(\mathbf{E}=-2 a(x \mathbf{i}-y \mathbf{j})\) (b) \(\mathbf{E}=-a(y \mathbf{i}-x \mathbf{j})\). Here \(\mathbf{i}\) are the unit vectors of the \(x\) and \(y\) axes. See Fig. 16 illustrating the case \(a>0\)