Magnetic Forces and Materials Questions and Answers

Answer: C

It is the magnetic counterpart of the electric polarisation, measured in amperes per metre, the same units as the field intensity. It enters the constitutive relation as \( \mathbf{B} = \mu_0(\mathbf{H} + \mathbf{M}) \).

Answer: D

From the constitutive relation and the definition \( \mathbf{M} = \chi_m\mathbf{H} \) it follows that \( \mu_r = 1 + \chi_m \). A vacuum has zero susceptibility and unit relative permeability, which is the check on the relation.

Answer: A

The applied field induces moments that oppose it, so the material is very slightly repelled from a field and its relative permeability is a shade below one. Copper, water and bismuth are examples, with susceptibilities of order minus ten to the minus five.

Answer: B

Permanent atomic moments align partially with the field, so the material is weakly attracted, and thermal agitation opposes that alignment, which is Curie's law. Aluminium and oxygen are examples, with susceptibilities of order plus ten to the minus five.

Answer: C

The exchange interaction aligns neighbouring moments over regions containing many millions of atoms, so a small applied field produces a very large magnetisation. Above the Curie temperature that coupling is overcome by thermal agitation and the material becomes paramagnetic.

Answer: D

Thermal agitation destroys the domain alignment and only the weak paramagnetic response of the individual moments remains. Iron's Curie point is about 770 degrees Celsius, which is why a transformer core must never be allowed to approach that temperature.

Answer: A

Exact cancellation leaves the material with almost no external magnetisation despite the strong internal ordering. Where the opposed moments are unequal the cancellation is incomplete and the material is ferrimagnetic, which is what a ferrite is.

Answer: B

Being an oxide it conducts very poorly, so the eddy currents that ruin an iron core at radio frequency scarcely flow. Its permeability and saturation flux density are both well below iron's, which is the price paid for that freedom.

Answer: C

Domains form because the alignment they impose costs less energy than the external field a uniformly magnetised body would produce. In an unmagnetised specimen the domains point in many directions and their moments cancel.

Answer: D

Domain walls move so that domains already close to the field direction grow, which needs only a small field. Only at higher fields does the magnetisation within a domain rotate bodily toward the applied direction, and saturation follows when all of it has.