Finding B, H, M in a toroidal permanent magnet with an air gap

[Qyzren]

The magnetic field inm the gap of the toroidal permanent magnet is 0.50 T. The length of the magnetic circuit is 20 cm and that of the gap is 1.0 cm.
what are the magnitudes of
i) B in the material
ii) H in the gap
iii) H in the material
iv) M in the material

The Attempt at a Solution

i) Assuming no "bulging of the field" B = 0.5 T
ii) B = μ0 * H => H = B/μ0
H = 0.5/[4π*10^-7] = 3.98*10^5 A/m

but for part iii & iv. I thought we need to know the permeability??
Is it possible to calculate H & M in the material without μr?

(i'm assuming they're looking for numerical answers rather than algebraic ones)

 

[Qyzren]

help? anybody? please?

 

[Meir Achuz]

mu has no meaning for a permanent magnet.
Use B=(mu0)(H+ M)
B in the gap equals mu0 M, so H in most of the magnet~0.