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

I will now resume my discussion of the first meeting of my Electromagnetic Theory class for the second week of the term.

When we discussed the vector or the cross product of two vectors, I first showed them how to get the components along the x, y and z axes since the result would have a magnitude as well as a direction unlike the scalar product which only had a numeric value.

Since this involves the sine of the angle between two vectors, unlike the scalar or dot product, then it is when the two vectors lie along the same axes that its value becomes zero, and is non-zero otherwise.

That means when distributing the values to the three components, only the operations involving the non-co-axial terms will be considered, which means no multiplication of values along the same axis exist.

Besides that, we used a very familiar method to determine the direction of the resultant vector: the right hand rule. After all, the application of this mnemonic that I taught them two terms ago (in the electricity and magnetism lecture - not the lab; that was application to the relationship between electric and magnetic fields) was derived from the cross product without me telling them directly that it was from the vector product.

Since unlike the dot product the cross product is not commutative, the thumb would represent the direction of the first vector and the index finger the second vector. The direction of the middle finger (when all three are held perpendicular to each other) would then denote the direction of the resultant.

Another method for determining the direction using the right hand rule involves moving the fingers in a sweeping motion from the direction of the first vector to the direction of the second vector. This time, it is the thumb that shows the direction of the resultant.

Since cross product is non cummutative, that means if the first and second vectors are reversed, then the direction of the resultant would be opposite that of the first.

I ended the lecture with some examples on how to solve for these two multiplications of vectors.

In the second meeting for the second week of classes for the same subject (which, I have mentioned before, happens an hour and a half later in the afternoon), I discussed three dimensional vectors and how to get the magnitude and direction of that (expressed in two angles instead of one for the two dimensional vectors) from the three components.

This involved the extension of the equations for two dimensions, but using the same principles of Pythagorean geometry.

Afterwards, I told them that we had just discussed translation from the Cartesian coordinate system to the spherical coordinate system (where one length and two angles are given to describe the distance or position of a certain point from the origin).

I then went on to describe conversion to the third coordinate system, which is cylindrical (involves TWO lengths and ONE angle).

We ended the day's (and week's) sessions with more exercises.

One of the students asked for a reference sheet with the formulas in anticipation of the first exam. Although historically, I have allowed them this before, this time I made it as a condition that everyone (all eight of them) show up on time for the afternoon session next week, since they trickled in belatedly from an apparently very long lunch.

It may be time to give them a quiz already with the existing coverage.

For now I'm of the mind that requiring more tests, exercises and homeworks while the topics are still easy (that means early in the term), and where there is a large likelihood that the students will get good percentages, will offset the probable low scores they might get in the later, built-up-on and more complicated lessons.

And that's the second week of classes. Next time I'll start discussing the start of the third week. Can I ask the last person left copying the notes to erase the board. Thank you, and goodbye for today.