Expanding Spherical Shell of Charge

in Gaussian units and in spherical coordinates where a(t) is the radius of the shell, Q is the total surface charge, and H(x, x0) = ∫ x −∞ δ(x ′ − x0) dx′ is the Heaviside step function. However, magnetic charges do not exist, so we cannot have a radial magnetic field of the form (1). That is, the magnetic field is zero, B = 0 everywhere, no matter what is the time dependence a(t) of the radius of the shell. Since there is no magnetic field, there is no Poynting vector, S = (c/4π)E×B = 0, and there is no radiation. This result was first crisply noted by Ehrenfest [3], and is an example where accelerated charges are not accompanied by electromagnetic radiation.