(a) A charge density ' of zero total charge, but with a dipole moment p, exists in...

(a) A charge density ρ' of zero total charge, but with a dipole moment p, exists in reference frame K'. There is no current density in K'. The frame K' moves with a velocity v = βc in the frame K. Find the charge and current densities ρ and J in the frame k and show that there is a magnetic dipole moment, m = (p × β)/2, correct to first order in β. What is the electric dipole moment in k to the same order in β?
(b) Instead of the charge density, but no current density, in K', consider no charge density, but a current density J' that has a magnetic dipole moment m. Find the charge and current densities in К and show that to first order in β there is an electric dipole moment p = β × m in addition to the magnetic dipole moment.