Theory
As the tape leaves the tape head, the applied bias partially offsets the tape's field and the remaining net induction is essentially the difference between the positive and negative half-cycles of the previously recorded signal. This differencing operation further cancels some of the nonlinearity. A constantly, rapidly varying magnetic field also helps overcome magnetic hysteresis (the tendency of paramagnetic materials to resist either being magnetized or releasing its magnetism) of both the recording head and the tape medium.
Read more about this topic: Tape Bias
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