I was wondering, does the optical activity of a material change under a magnetic field? Assuming it did, how would one analyze this phenomenon in the eyes of classical electrodynamics or classical optics? I do not require a specific theory but a little push of inspiration would be much appreciated. Thanks.
Yes, optical activity can be affected by external electric and magnetic fields. Check out the Faraday effect:
Explanation of this phenomenon can be attempted with the assumption that the external magnetic field changes the electronic motion inside the molecules in such a way as to modify their effect on the macroscopic EM field. There are models of molecules that try to quantify this, both classical and quantum-theoretical. Details are quite complicated and computationally difficult, unfortunately - the microscopic theory of optical activity seems far from being an accomplished subject.