Question

do em waves interact with external electric or magnetic fields?why or why not?
if yes,then can visible light be bent by using external electric or magnetic fields?

Answer 1

Dear Student,

The direct reason for this is because in vacuum, where all the charges and currents are zero, Maxwell's equations are coupled, linear equation in E and B field. Now we know from theory of differential equations that for a linear differential equation, given two solutions, its linear combination is also a solution. So interaction of e.m wave with external field has to be in such a way that it respects linear superposition principle. Now if you expand your fields as E=Ee.m+Eexternal E=Ee.m+Eexternal and B =Be.m+Bexternal B=Be.m+Bexternal and with little bit of algebraic manipulation with Maxwell's equations you can show that if linear superposition is to hold, the external fields should not source the electromagnetic field. This is if you wish the reason from classical physics as to why electromagnetic waves are not deflected by external fields or as others have put it, photons do not interact with or scatter each other. But this is not the case with quantum mechanics. In quantum electrodynamics, photons do interact with other photon through exchange of fermions.

Regards