Problem 3.365

In an inertial reference frame \(K\) there is only electric field of strength \(\mathbf{E}=a(x \mathbf{i}+y \mathbf{j}) /\left(x^{2}+y^{2}\right),\) where \(a\) is a constant, \(\mathbf{i}\) and are the unit vectors of the \(x\) and \(y\) axes. Find the magnetic induction \(\mathbf{B}^{\prime}\) in the frame \(K^{\prime}\) moving relative to the frame \(K\) with a constant non-relativistic velocity \(\mathbf{v}=v \mathbf{k} ; \mathbf{k}\) is the unit vector of the \(z\) axis. The \(z^{\prime}\) axis is assumed to coincide with the \(z\) axis. What is the shape of the magnetic induction \(\mathbf{B}^{\prime} ?\)