Sorry for the late reply, I didn't see the notification in mt emails. Thanks for the very detailed answer though. Jackson's explanation is quite smilar to your first one, although he doesn't mention that you can always add a derivative which is useful to know.
Thank, you. I'll take a lok if I can find a version online.
Do you know what is meant when Jackson says the stress energy tensor is not gauge invariant? For me, gauge invariance is when a change inthe potentials doesn't change the fields, but this is different from the fields. Is it to do with...
Hi, I hope this is in the right section. It's for EM which I guess is a relativistic theory but the question itself is not to do with any Lorentz transformations or anything similar.
I'm reading through Jackson with my course for EM and I'm on the section where he is generalising the Hamiltonian...
Thanks for the reply. What do you mean by an r-process?
So, I emailed my professor and I see where I may have made a mistake in my calculation. If you calculate the energy of the nuclei using E=mc^2 then there is more energy in the alpha and Nickel nucleus than in the Zinc.
So, if what we...
I know it's a common question but I've found no answers online so far. My professor has made a point out of saying that fusion reactions after iron and nickel do release energy but just not enough to keep the star from imploding. This didn't make sense to me. How would fission release energy if...
We've just gone over the EPR paradox in class and I'm not really satisfied by the explanation of the professor and TA.
Firstly, with the example of the two spins, I still don't see why measuring one spin and then knowing the other one doesn't count as information traveling faster than light...
OK, thank you for clearing this up for me! I think a lot of my confusion came from the fact that I couldn't imagine how the fields can carry the energy into the wire without them themselves moving.
Ahh yeh, sorry, I don't know what I was thinking. I forgot you could derive the surface charge from the continuity equation, and of course the surface charge produces a radially outward field. Thanks for the link to the paper, it explains it pretty well!
One thing I didn't quite understand is...
So how are the fields carrying the energy in from the outside? Especially for the electric field since it is zero outside.
I'm pretty sure there's meant to be no surface charge on the wire. The electric field is created by the potential difference. A surface charge on a cylinder would create a...
If we have a some wire (length L) with a PD of V from one end to the next and a current I moving along it we can work out the Poynting vector. It's pointing radially inwards and so tells you the energy per unit time per unit area flowing into the the surface of the wire.
What I don't understand...
Ah OK, I'm still not 100% sure as to why the integral doesn't work, but I guess I've set the problem up wrong. Theoretically, there's no reason why you shouldn't be able to do the integral in spherical coordinates (although it'll be a lot more complicated), so I think if I do I should get some...
That's what I tried to use (except I didn't set r to 0 from the start though it shouldn't matter surely?). The integral I ended up getting (just for the interval 0 to pi for phi) was:
V(r)=PR2/(4πε0)∫0π∫0π (cos(φ)sin(θ))/√(r2-R2-2rRcos(θ)) dθdφ (sorry about how it looks, still trying to get...
I kept r (the vector from the origin to the point I want to find the potential at), just as r. But since we are not integrating over r I don't think that would matter.
I also set the r' in the integral equal to R, since all the surface charge is at a distance R.
Thanks for the link, although on...