Question

Can Maxwell's equations be derived using only Coulomb's Law and Special Relativity?

If so, and the B
-field is in all cases a purely relativistic effect, then Maxwell's equations can be re-written without reference to a B
-field. Does this still leave room for magnetic monopoles?
A) Yes, Maxwell's equations can be derived from Coulomb's Law and Special Relativity, and the absence of explicit B-field references leaves room for magnetic monopoles.
B) No, Maxwell's equations cannot be derived solely from Coulomb's Law and Special Relativity, and the absence of B-field references doesn't allow for magnetic monopoles.
C) Yes, Maxwell's equations can be derived using Coulomb's Law and Special Relativity, but the absence of B-field references negates the possibility of magnetic monopoles.
D) No, Maxwell's equations cannot be derived from Coulomb's Law and Special Relativity, however, the absence of B-field references still allows for the existence of magnetic monopoles.

Answer 1

Maxwell's equations can be derived using Coulomb's Law and Special Relativity, however, this derivation does not eliminate magnetic fields (B-fields) nor does it suggest the existence of monopoles, which would require a modification to Maxwell's equations. Therefore, the correct option is C).

Step-by-step explanation:

Maxwell's equations can indeed be derived from Coulomb's Law and Special Relativity. By applying Lorentz transformations to electric fields, magnetic fields naturally emerge as a relativistic effect. Coulomb's Law, when combined with the principles of relativity, leads to full electromagnetic wave equations. These wave equations implicitly include the magnetic field (B-field), as electric and magnetic fields are related and are manifestations of a single electromagnetic field. Maxwell's equations, when derived in this way, still inherently include the B-field, and the discovery of magnetic monopoles would require an extension or modification of these equations.

Therefore, the absence of B-field references in the derived equations does not negate the possibility of magnetic monopoles. Instead, the current formulation of Maxwell's equations, even when derived using relativity, does not accommodate monopoles because the equations assume the absence of magnetic charge sources, consistent with the observed continuity of magnetic field lines. The potential existence of magnetic monopoles would imply a symmetry in Maxwell's equations that is not currently observed. Based on the information provided, the answer is C) Yes, Maxwell's equations can be derived using Coulomb's Law and Special Relativity, but the absence of B-field references negates the possibility of magnetic monopoles since the standard form of these equations already assumes there are no monopoles.