Write expressions for the magnitudes and directions of the electric fields measured in Problem 24.

Data from Problem 24

A positively charged particle is at rest on the positive \(z\) axis in reference frame \(S\). Reference frame \(S^{\prime}\) is moving along the positive \(x\) axis of \(\mathrm{S}\), reference frame \(\mathrm{S}^{\prime \prime}\) is moving along the negative \(x\) axis, and reference frame \(\mathrm{S}^{\prime \prime \prime}\) is moving along the \(y\) axis, all with speed \(v\) relative to \(\mathrm{S}\). The axes of all the reference frames are oriented the same way, and their origins coincide at instant \(t=0\), when observers in each reference frame make measurements. In which reference frames do observers measure an electric field?