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 $\mathbf{E}^{\prime} ?$