Magnetic force between two parallel moving charges

[Philip Wood]

Exactly so. When psi = pi/2, i.e. in the transverse direction, (1 - beta^2 sin^2 psi)^3/2 becomes (1 - beta^2 )^3/2 = gamma^-3, so the transverse E in the lab frame is simply gamma times that in the rest frame of an electron. We can reach this result very simply by applying length contraction to a coin-shaped gaussian box with an electron at its centre.