Relations Among B, H, M, Susceptibility, and Permeability
In SI for a linear isotropic medium, B = mu_0(H + M), M = chi_m H, and B = mu H. Therefore mu_r = mu/mu_0 = 1 + chi_m.
Why this shows up in the exam
Converting susceptibility to permeability · Finding H from B in a material · Computing material-induced field changes
Learn the idea
In a linear magnetic medium, susceptibility links M to H and relative permeability equals one plus susceptibility. The applied current creates magnetizing field H, while the material adds magnetization M. Their combined effect determines magnetic flux density B.
🧠 Memory hook: Relative mu is one plus chi.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- B = mu₀(H + M) — general SI relation between flux density, field, and magnetization
- M = chi_m H — definition of volume susceptibility in a linear medium
- mu_r = 1 + chi_m — relative permeability-susceptibility relation
- mu = mu₀ mu_r — absolute permeability
How to approach it
- 1Write the requested quantity with units
- 2Choose B = mu H or B = mu₀(H+M)
- 3Convert between absolute and relative permeability only once
Common slip-ups that cost marks
- •Writing chi = mu_r/mu₀ - 1
- •Mixing B in tesla with H and M in A/m
- •Using linear relations for strongly hysteretic states without qualification
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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