In a chapter building up to the theory of plane waves my book starts by introducing time harmonic electric fields and defines a special case of Gauss's law. curl(H) = J + dD/dt curl(H) = sigma * E + epsilon * dE/dt if E is time harmonic and spacially dependent... E(x,y,z,t) let E' represent the phasor form curl(H) = sigma * E' + epsilon * j * w * E' curl(H) = (sigma + epsilon*j*w) E' of curl(H) = jw(epsilon - j*sigma/w) E' where epsilon - j*sigma/w = epsilon_c (complex permittivity) given that... divergence(curl(H)) = 0.... divergence( jw * epsilon_c * E') = 0 therefore divergence(E) = 0 so pv (volume charge density) = 0 by Gauss's law I am very confused why a time harmonic E field can never bound a charge source and why it's divergence is always zero as my book seems to suggest. I am guessing of have missed a major assumption and or am misinterpreting something? Looking for some guidance. Thanks!