Problem 3.364

In an inertial reference frame \(K\) there is only magnetic field with induction \(\mathbf{B}=b(y \mathbf{i}-x \mathbf{j}) /\left(x^{2}+y^{2}\right),\) where \(b\) is a constant, i and \(\mathbf{j}\) are the unit vectors of the \(x\) and \(y\) axes. Find the electric field strength \(\mathbf{E}^{\prime}\) 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 field \(\mathbf{E}^{\prime} ?\)