Recent content by Rick16

This is very helpful, thanks a lot.

Thank you everybody for your help. It all begins to make sense now. Griffiths even puts the equation ##\nabla \cdot (\frac{\hat r}{r^2})=4\pi\delta^3(r)## in a box. There are 108 numbered equations in chapter 1, only 5 of which are boxed. The other ones are the definition of the nabla operator...

This looks very convincing, but do you really go through all this everytime you are confronted with this kind of situation? Griffiths simply isolates the term ##\frac{\hat r}{r^2}## and then uses the relation ##\nabla \cdot \frac{\hat r}{r^2}=4\pi \delta^3 (r)##. At first, I did not understand...

Should I draw the conclusion that whenever I have a vector field in spherical coordinates with ##r^2## in the denominator, I cannot mechanically apply the above expression for the divergence, and that I should instead try to isolate ##\frac{\hat r}{r^2}##, which then gives me an expression for...

I have looked back at section 1.5 in the book, but it has not helped much so far. Apparently there are situations when the general expression for the divergence in spherical coordinates $$\nabla\cdot \vec v=\frac {1}{r^2}\frac {\partial}{\partial r}(r^2 v_r)+\frac {1}{r \sin \theta}\frac...

TL;DR: Griffiths, problem 2.46 Here is the problem statement: The electric potential of some configuration is given by the expression ##V(r) = A \frac {e^{-\lambda r}} {r}##, where A and lambda are constants. Find the electric field E(r), the charge density ##\rho(r)##, and the total charge...

At my university, we could choose between 3 different tracks. Once a track was chosen, there was no more flexibility, no electives.

So, basically, the advice that I am getting is that I should wait and see, take one step at a time. That is certainly reasonable. On the other hand, when you go to college, you know what material you are going to study for years to come. I have always liked this aspect, having a curriculum, and...

I have checked those, but I am not looking for big, authoritative books, rather for accessible ones, books that are student-friendly, well suited for self-study. A case in point would be Jackson, which may be a bible, but from what I have heard is not a good book to study from. Klauber, on the...

I got a bachelor in physics 11 years ago, and I did not continue my studies. I have now decided to embark on a complete review of undergraduate physics, on my own, as a hobby. I have chosen 7 books for this purpose: Mary Boas: mathematical methods in the physical sciences John Taylor...

Okay, my idea about the external torque is pretty far-fetched. I think I am rather convinced that there is no external torque acting on the saucer. Now I wonder what would happen if somebody built such a thing. It should not be difficult to build a rotating disc, it wouldn't even have to lift...

So there would be a reaction torque on the fuselage similar to the reaction torque on the car. Very clear explanations, thank you.

Very interesting, I never thought of it that way.

I meant to say that the energy is ultimately responsible for the torque, and that therefore the torque might be considered external to the system, i.e. the saucer.

Here is the full paragraph: All this leaves me saddened to report that smooth, rotating flying saucers are not a thing. They violate the conservation of angular momentum, which is physics-speak for declaring they cannot spontaneously spin up and spin down without some other thing to counter the...