Final answer:
Gauss's Law explains why electric fields are zero inside a conductor due to electrostatic equilibrium. In contrast, magnetic fields, described by Ampère's Law and Maxwell's Equations, remain as they form continuous loops and do not have magnetic monopoles, which prevents a similar equilibrium inside a conductor.
Step-by-step explanation:
The absence of electric fields in a conductor is explained by Gauss's Law, which is a consequence of the fact that electric field lines originate on positive charges and terminate on negative charges. When electrostatic equilibrium is reached within a conductor, the free charges distribute themselves in such a way that they cancel the electric field within the material, leading to a net electric field of zero inside.
However, magnetic fields behave differently due to the nature of magnetic field lines and the fact that no magnetic monopoles have been observed. Magnetic field lines are continuous loops with no beginning or end, which is why a similar cancellation effect does not occur with magnetic fields as it does with electric fields inside conductors. Ampère's Law, another of Maxwell's Equations, concerns the magnetic field created by electric current and does not have a counterpart to the electrostatic equilibrium that leads to a zero electric field within a conductor.