Interaction of the oscillating magnetic field of electromagnetic radiation with a molecule or atom Whenever we read rotational, vibrational and electronic spectroscopy, we find details on the interaction of the electric dipole moment of the molecule with the oscillating electric field of electromagnetic radiation. The selection rules are also derived on the basis of transition dipole moment operator on wavefunctions. I was talking to spectroscopists today and asked that why do spectroscopy textbooks (and authors) do not mention anything about oscillating magnetic field of light waves. The magnetic field also carries the same energy as the oscillating electric field. Doesn't that interact with electrons as well?* They said that interaction of the magnetic field with a molecule's electric dipole is very weak and hence nobody mentions about it. Does anyone have a good reference or an equation which shows that the oscillating magnetic field interacts very weakly with the molecule's electric dipole moment? They were mentioning Fermi's golden rule and at this stage I lost them.

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* Electron spin resonance is an example.
The magnetic dipole transition intensity is typically about $10^5$ times smaller than the allowed electric dipole but as this can vary by ten orders of magnitude, second order transitions (with terms $x^2,y^2$ etc ) as well as magnetic dipole transitions can occasionally be important. The electric dipole matrix element  is $\langle a|\hat r|b\rangle$, where $\hat \mu =e\hat r$, the  second order dipole $\langle a|\hat r \hat r|b\rangle$ and magnetic dipole $\langle a|\hat J|b\rangle$ where $\hat J$ is the angular momentum operator 
$\displaystyle \sim \langle a|z\frac{\partial}{\partial x} - x\frac{\partial}{\partial z} |b\rangle $.
The transition intensity is the square of these terms and the selection rules differ for each type of transition. A derivation is given over several pages by Steinfeld 'Molecules and Radiation' chapter 1, 2nd ed (publ MIT Press).