Maybe I shouldn't have started this blog now, not with everything that's been going on.

School year 2004-5, Trimester 3, Week 13, Meeting 1 & 2, Electromagnetic Theory class: Our last three topics were current, current density and magnetic field.

The definition of current, contrary to the simplified version I gave them in Electricity and Magnetism class, is really a derivative of the charge with respect to time. Or, charge is the integral of the current through a certain cross sectional area over a period of time.

Unfortunately the only example I could give them for this type of problem used the analogy of the rate of volume going through a water hose as “current”. The volume per unit time had to be converted by the value of density of water to mass per second. Using the water’s molar mass, it now became moles per unit time. Taking into consideration Avogadro’s number (some of the students cringed at a throwback to their chemistry classes) the value as turned into molecules per second. Knowing the number of electrons per molecule of water (one for each of the two atoms of hydrogen and eight for the one atom of oxygen) and multiplying by the charge of the electron, we were able to obtain the charge per unit time, which, of course is just the current.

Another formula for current that uses current density was given: the integral of the dot product of the current density and the infinitesimal area.

I gave one example where the current density is given as changing as one goes further from the axis of the wire, and only taking the current from half the radius outward. The area had to be taken as the circumference of the thin ring integrated over.

After that, I gave them an exercise where again the current density was given (maximum at the axis and zero at the surface) and they had to show that the current was a certain value (of course I gave the answer already in the book so that they would know immediately if they solved it correctly or not).

In the afternoon I gave them the opposite of the morning’s problem: where the current density is maximum at the surface and zero at the center axis. They were able to solve it in twenty minutes, and then we went to our last topic.

In magnetic fields, there were three cross product formulas. One was for the magnetic force from the cross product of the product of the charge and its velocity, and the magnetic field it is traveling in.

The second, for the force induced by a conducting wire, is the cross product of the product of the current and the vector length of the wire, and again the magnetic field.

For a coil of wire caused to spin in a magnetic field, the torque (or rotational force) is the cross product of magnetic dipole moment and once more the magnetic field. The magnetic dipole moment, represented by the Greek letter “mu”, is the number of turns of the coil times the current times the area enclosed, and its direction is given by the right hand rule just as with the cross product.

The last formula I gave them was for the magnetic potential energy, with is the negative of the dot product of the magnetic dipole moment and the magnetic field.

I’ll talk about the make up of the mechanics lecture students tomorrow. For now, class dismissed.