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An ideal solenoid has a core of relative permeability 500 and its winding has 1000 turns per metre. If a steady current of 1.5 A is passed through its winding, find (i) the magnetization M_(z) (ii) the magnetic induction B within the solenoid. Assume that M_(z) is directly proportional to H and single valued. |
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Answer» Solution :Data: `mu_(r )=500, n=1000 m^(-1), I=1.5A, mu_(0) = 4pi xx 10^(-7) T.m//A` The magnetic field strength (or magnetic intensity) of the ideal solenoid, `H=nI = 1000 xx 1.5 = 1.5 xx 10^(3) A//m` (i) The magnetization of the core, `M_(z) = X_(m)H=(mu_(r)-1)H` `=(500-1) xx 1.5 xx 10^(3)` `=499 xx 1.5 xx 10^(3) = 7.485 xx 10^(5) A//m` (II) The magnetic induction WITHIN the core of the solenoid, `B=mu_(r)mu_(0)H` `=(500)(4 xx 3.142 xx 10^(-7)) (1.5 xx 10^(3))` `=30 xx 3.142 xx 10^(-2) = 0.9426` T |
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