Question

Relativistic Electrodynamics

Please solve this question EXACTLY as the hint describes, NOT using potentials.

Calculate the electric and magnetic fields of a point charge that is moving with velocity v. Determine the time-dependence of the electric and magnetic fields seen by the observer. When are the fields maximal? Sketch the electric field lines for the moving charge in the observer frame and in the rest frame.

Hint: Choose a coordinate system S, in which the charge is moving along the positive x axis and an observer P is at rest at a point on the y axis. Choose a rest frame S' of the charge, in which the axes coincide with the axes in S at t = t' = 0, determine the electric field in S' at the position of the observer, and transform back into S. Express the result in terms of the velocity of the particle (and derived quantities β and γ), the distance to the charge and the angle between velocity and the vector pointing from the charge to the observer in the rest frame of the observer.

Answer 1