Yes that was a typo. They should be written:
E2 - E1 = Integral[dQ , from state 1 to state 2]
E1 - E3 = Integral[dQ , from state 3 to state 1] + 7 P1 V1
One idea: I can calculate Cv = (dE/dT)_V = a g T^(a-1) V , and I also know Cv = T (dS/dT)_V which helps me know a little bit about the change...
My attempted solution is as follows:
Obviously the heat transfer happens during transitions 1->2 and 3->1.
It's also clear that
P1 = P3
V1 = V2
E2 - E1 = Integral[T dQ , from state 1 to state 2]
E3 - E2 = - Integral[P dV , from state 2 to state 3]
E1 - E3 = Integral[T dQ , from state 3 to...
Agreed! Also, Jackson's previous sections (e.g., 3.9) had ALREADY performed an expansion via eigenfunctions when he derived the Legendre equation from the Laplacian in spherical coordinates and then connected the eigenfunction expansion to 1/|x-x'| in terms of the spherical harmonics...
Yes this post is looking only at electrostatics; the conversation was always clarified to be been limited to electrostatics; and it was mentioned a couple times that the scope of Green's functions was limited accordingly. So yes, it seems we are limited to Green's theorem's that have a lone...
Ok, then what other purpose do those extra ## f(x) + \lambda## terms serve? Green's theorem in equation 1.35 has only a Laplacian operator. It seems that it doesn't allow other linear operators to enter in -- only a Laplacian. So can you explain why the extra ## f(x) + \lambda## would ever be...
How do you know they aren't related to the boundary conditions?
The fact that they are "part of the linear differential operator" is irrelevant to whether they are related to the boundary conditions or not.
Jackson explains that the core fundamental operator for Green's functions for...
Insofar as Jackson's explanation of Green's functions goes, Green's functions only need to satisfy L_x G(x,x') = \delta(x-x') -- see Chapter 1, especially equation 1.31. Jackson's explanations of Green's functions give no reason to pursue arbitrary operators like ##\nabla^2 + f(x) + \lambda##...
Moving onto the second part of my questions about section 3.12:
Why is "the z coordinate is singled out for special treatment" in equation 3.168? A rectangular box needs ALL of the bounding planes to have a boundary condition correct? So why would Jackson single out just the z-direction for...
Thank you Vanhees71,
Yes I understood your point, thanks, but let me drill down directly at my confusion:
I thought the methodological approach for using a Green's function to solve an electrostatics problem went via the following steps, in order of operation:
1) create a representation of...
Orodruin and all, attached are pdfs of the relevant sections of the book, but there may be context or information missing, so please let me know if you want other sections uploaded.
Hi wizards,
I'm working through Jackson's book on E&M (3rd edition) and got stuck in section 3.12 on expansions of Green functions. I have three questions regarding section 3.12:
First, why is Jackson trying to find a Green function that satisfies equation 3.156? To my beginner mind, it...
It seems the answer is "it's a completely non-interacting sphere near a point charge"... which seems to be a very useless, rarely occurring, seldom-real-world-application, mathterbation example for Jackson to spend our time on.
Please continue on to answer my follow on questions: "if it's NOT a conducting sphere then what is the interaction between the "nearby point charge" and the sphere? Is it a dielectric sphere? Is it a completely non-interacting sphere?"
Hi , I'd like a little bit of clarification about Section 2.6 from Jackson's classic book on E & M.
Section 2.6 starts out with the problem of a "conducting sphere" near a point charge, but then it confusingly veers away to a problem where potential is prescribed to vary with azimuth and polar...