what happens to the magnetic field during linear polarization and what happens exactly?
Well, "polarization" usually refers to the direction the E-field is pointing. In a vacuum, the B-field would be perpendicular to the E-field, but in matter, this is not strictly the case.
The magnetic field will be at right angles to the electric field and will vary in amplitude in phase with the Electric field. Both field vectors will be at right angles to the direction of propagation of the wave.
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