Question

what is the value of magnetic field inside an metallic cage?

Answer 1

The magnetic field will be close to zero only if a high permeability metal is used. The most effective one is called mu-metal . Once the box is placed in the field, it enters the metal on one side of the box, and exits on the opposite side. It is easier for the field to go along the metal rather than through it. This is just a simple-minded discussion of what happens, but it gets the idea across.