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