. cl as s - ph ] 1 5 A ug 2 00 5 Faraday ’ s law in the presence of magnetic monopoles

We show that if we consider the full statement of Faraday's law for a closed physical circuit, the standard Maxwell's equations in the presence of electric and magnetic charges have to include in their integral form a mixed term of the form ρ m v ⊥ e where ρ m is the magnetic charge density and v ⊥ e the perpendicular component of the velocity v e of the electric charge. Maxwell's electrodynamics with its model role for a fundamental theory [1] and its numerous applications is one of the most successful theories in physics [2, 3]. The equivalence between Maxwell's laws in integral and differential form is evident in the derivation of the latter from the former and manifest in the claim that the Maxwell's equations in differential form together with the Lorentz force encompass the whole of electromagnetism. The integral form of Faraday's law plays a special role in this context. Let us consider a real closed physical circuit with moving boundaries. If we wish to include the motional induced electromotive force (emf) in the Faraday's law, the boundary of the surface integral in this law becomes time dependent. In such a situation the velocity v pull which is controlled externally can depend both on position and time, i.e., v pull = v pull (t, r). It is not difficult to start with the Faraday's law with a time dependent boundary which encompasses the motional induced emf to derive the third Maxwell's equation in differential form. However, this procedure requires a mathematical identity for differentiating surface integrals in which the divergence of the magnetic field will appear. One of the reasons why the above mentioned general equivalence of the differential and 1