(a) Use the four-vector character ofand the Lorentz transformation laws for B and E to deduce that the scalar and vector potentials form a four-vector (A, iϕ/c). This reverses the methodology followed in the text.

(b) Show that the spherical equipotentials of a stationary point charge distort to ellipsoids when the charge is in uniform rectilinear motion with velocity v. Plot a cross sectional view of one equipotential on the same graph for v = 0.3c, 0.5c, 0.7c, and 0.9c.