By definition, the flux ΦB of magnetic induction B through the surface S is (if the magnetic induction is constant):
ΦB=Bn⋅S, where Bn is the normal to the surface component of the electromagnetic induction. As far as the rod is long and rather thin, one can assume, that the magnetic induction is constant inside the rod and directed along it's axis. Thus, the magnetic induction will be:
B=Bn=ΦB/S=1.96⋅10−4m210.05⋅10−4Wb=5.13T
The intensity of magnetising field is:
H=μrμ0B, where μr=1000 is the relative permeability of iron and μ0=1.26⋅10−6H/m is the magnetic permeability of free space. Thus:
H=1000⋅1.26⋅10−6H/m5.13T=4.07⋅103mA,
By definition, the magnetisation then will be:
M=μ01B−H=1.26⋅10−65.13−4.07⋅103≈4.07⋅106mA
Answer. M = 4.07*10^6 A/m, H = 4.07*10^3 A/m.
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