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Recently I learnt about shielding a region of space from an electric filed. I wondered if the same can happen for magnetic field.

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Superconductors are excellent magnetic shields - a hollow superconducting sphere can prevent magnetic fields from entering (up to a certain level). Similarly, there is a class of materials called "mu metals" which have a high permeability - that is, they 'suck' magnetic field lines towards them to that the region inside a mu metal shield will have much weaker magnetic field (up to the point where the mu metal saturates). This is used, for example, to protect PMTs (photomultipliers) from the earth's magnetic field (the electrons would be bent by the earth's field, thus affecting the gain as a function of orientation).

There are two examples of the magnetic equivalent of a Faraday cage.

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