Question

If magnetic monopoles would have existed. How would the Gauss' law of magnetism be modified?

Answer 1

A magnetic monopole needs to be analogous to an electric monopole. A stationary electric monopole produces no magnetic field, so a magnetic monopole can produce no electric field. Therefore Gauss's law for electricity is unaffected,

$\nabla .E=\frac{\rho }{{ϵ}_0}$

and Gauss's law for magnetism takes an analogous form,

$\nabla .B={\mu }_0{\rho }_m$