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.

Explanation

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