## Thursday, May 22, 2008

### Magnetism

Back from Dubai, I'm working hard to complete my second OU assignment for SMT359 - Electromagnetism. Seems like no sooner is one finished and dispatched than the next one hoves into view. The current set of questions are not all calculations - there are also essays like the one I am about to inflict upon you, which asks the student to describe the microscopic and macroscopic reasons for different kinds of magnetic materials. Here is my answer.

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When current flows around a closed circular loop, it creates a magnetic field which is similar, at a distance, to that from an electric dipole. The current-carrying loop is therefore, by analogy, called a magnetic dipole.

The magnetic dipole moment (MDM) is defined as m = IΔS, where I is the current in the loop and ΔS is the area enclosed by it; m is a vector oriented normal to the area ΔS in a direction determined from the current direction by the right-hand rule.

Atoms (and molecules) can also be magnetic dipoles, with MDMs. Classically, these MDMs derive from two sources: the orbital motion of the electrons around the nucleus, and the spin of the electron around its own axis. (The contribution from the spin of nucleons is far less and can be ignored).

Permanent Dipole Moment

The MDMs from orbital motion and spin add vectorially, and may reinforce each other, or cancel to zero. Atoms and molecules with non-zero intrinsic MDMs are said to have a permanent dipole moment. The permanent dipoles tend to align with any applied field, reinforcing it.

Induce Dipole Moment

When an external magnetic field is applied to an atom, it creates a distortion in orbital motion, effectively an induced current which by Lenz’s law, tends to oppose the applied field and reduce it. The induced electron orbital current persists as long as the field is applied and creates an induced magnetic dipole moment.

Magnetization

The magnetization of a material is a vector quantity M which gives the total magnetic dipole moment per unit volume. Its definition is M = n<m> where n is the number of magnetic dipoles per unit volume and <m> is the average value of the dipole. Because the MDM is a vector, if individual atoms or molecules have their MDMs oriented randomly, the average value will be zero. An applied field can tend to align atomic/molecular magnetic dipoles - (parallel to the applied field for permanent dipoles, and anti-parallel for induced dipoles), but the field has to contend with random thermal collisions which tend to disrupt such alignment. Typically M tends to be proportional to the applied magnetic field and inversely proportion to the absolute temperature.

Magnetic Material Types

Diamagnetic materials are materials with very small to zero permanent dipole moments. When an external magnetic field is applied, induced magnetic dipoles are created which resist it. The magnetic field close to, and within the diamagnetic material is therefore weaker than the applied field.

Paramagnetic materials are constituted from atoms or molecules with permanent magnetic dipole moments. These tend to align with an applied magnetic field, thermal jostling permitting, reinforcing it. The magnetic field close to, and within the paramagnetic material is therefore stronger than the applied field.

Finally there is the special case of ferromagnetism. Normally magnetic dipoles close to each other, like bar magnets, will not align in the same direction. The lower energy configuration is to align anti-parallel. However, for quantum-theoretic reasons, in ferromagnetic materials the optimal configuration is for the dipoles to align in the same direction, at least within small volumes called domains. An applied magnetic field can align the domains themselves to the direction of the applied field, and this alignment can persist after the field is removed, a phenomenon called permanent magnetisation. The magnetic field close to, and within the ferromagnetic material is significantly stronger than the applied field.

If the temperature is increased in a ferromagnetic material past the Curie temperature, (~ 800 degree C for iron), thermal energy will disrupt the quantum-mechanical coupling between adjacent dipoles and the material reverts to being paramagnetic.

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I have failed to get this down to 40-500 words: it's just over 600.