Student "edition" found at {csi dot journalspace dot com}.

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

In my most recent Electromagnetic Theory lecture class, we talked about Gaussian surfaces and electric flux, which again is just a review for them – at least, for the symmetric scenarios we discussed before with a point charge at the center of a sphere or a cube, or a line of charge whose nearest points are the same distance from an imaginary cylinder surrounding it.

But this time around, we talked about non-symmetrical situations and their closed integrals.

I was surprised that it was the first time that they encountered the closed integral sign, which looks a bit like a G clef – the normal integral sign with a circle in the middle.

We also began with the situation of a point charge symmetrically at the center of a cylinder of charge, which is familiar and at the same time altogether new.

We got the integrals for the two surfaces on either end of the tube, which –unlike the line of charge – is not equal to zero because of the electric field lines are not along the plane of the surface. Since it is a cross product, they had to get the cosine of the electric field lines relative to the vector normal to the plane.

Since it is a surface, that meant we would have to get a double integral, and because the areas are circular, one of the integrals had to be for changing radius.

The inner integral is for the entire circumference of each ring, so it was constant with respect to the changing length, but still the same distance from the charge.

This was a relatively easy integration which was the same as several of the previous integrations we had completed before, with two terms squared in the denominator raised to three halves, just the numerator changing.

The result was the same for the left as well as the right, so we moved to the integration of the roll (open at both ends) afterwards, again a double integral, but this time with the radius constant, and can be taken to half the length and just doubled.

At this point a certain student, still not listening even though he somehow maneuvered to sit at the center (and wasn’t copying either) asked what the subscripts I was writing meant (L for left, R for right, C for cylinder and T for total) which I just passed on to the other students to answer as bonus points since they were paying attention. Will that hurt is grade conscious sensibility?

Session 1525 is still not alert. Class dismissed.