When a certain material is cooled below its critical temperature, it exhibits the Meissner effect and completely expels all magnetic field lines from its interior, acting as a perfect diamagnet. What are the exact values of the magnetic susceptibility ( ) and relative permeability ( _r ) for this material in this state?

Step-by-step solution

For a material exhibiting the Meissner effect (a perfect diamagnet), the magnetic field inside the material is exactly zero ( B = 0 ). The magnetic induction is given by B = ₀ _r H . Since B = 0 and the external field H 0 , the relative permeability must be zero ( _r = 0 ). Using the relation between relative permeability and magnetic susceptibility, _r = 1 + . Substituting _r = 0 , we get 0 = 1 + = -1 . Thus, the magnetic susceptibility is -1 and the relative permeability is 0 . Answer: = -1 , _r = 0