Inertial system S' is moving away from inertial system S with relative velocity v_n, where u is the relative speed and n is the unit vector pointing in the direction of motion. Let us use the subscript l to refer to quantities along the line of n. Moreover, let us use the subscript ⊥ to refer to quantities perpendicular to the line of n. In this regard, we may respectively express the electric and magnetic fields in system S as E = E_A + E_B = B_n + B, where E_j := E · n and B_j := B · n. For a boost from system S to system S' along the direction n, we find that E' = E_Ei = (E + v_n × B) and B' = B_B = 1/(B - E), where γ = (1 - v^2/c^2)^(-1/2).
(a) Show that if E = 0 in system S, then E' = B' in system S.
(b) Show that if B = 0 in system S, then B' = -E'/c^2 in system S.
