Clearly, they used the binomial expansion on this; however, I cannot figure out why [G] is sandwiched by the epsilon inverses:
$$\varepsilon^{'-1}=1/(\varepsilon+i\epsilon_{0}[G])\approx(1-i\epsilon_{0}[G]\varepsilon^{-1})\varepsilon^{-1}$$
I am modeling the basic Tesla coil circuit. In particular, it is this one:
The resistor isn't shown in this diagram, however. I am treating the spark gap as a capacitor, whose voltage drops to zero once the voltage across it reaches ##V_o##. I actually entered the first equation wrong--its...
Honestly not sure how to go about this. Again this is one equation of 4 that I have. I considered using Laplace transforms but taking the Laplace transform of a step function whose argument is one of the variables being solved for doesn't seem possible. Also, if there is an alternative way to...
That's an interesting way to solve. Could you show what you did? But if someone was familiar enough with Poisson's equation, you could solve it that way with the point charge being a delta function in terms of charge density. The uniqueness theorem guarantees a solution as long as the charge...
I understand what you are saying; however, the cylinder does not represent the neutral conducting rod in the original problem. The problem I proposed only has a cylindrical shell with different potentials on the top and bottom half, nothing else.
This is similar to a point charge above an...
When using the method of images, it is my understanding that you look for a situation that satisfies the same boundary conditions that the original problem does, but is easier to solve. In what I presented, I did exactly that. Where I am not confident is the fact that I never actually used any...
I believe the solution is to replace the problem by a cylinder of radius R (I'm using R instead of r for clarity) where the top half (##\phi## going from 0 to ##\pi##) is at potential ##+V_{0}## and the bottom half (##\phi## going from 0 to ##-\pi##) at ##-V_{0}##. Once you have done this, the...
I have had this same question as well. I believe it has to do with boundary conditions for the magnetic field. If you use the boundary conditions on ##\vec H## and ##\vec B## at an interface of two linear materials, you get the relation ##\tan\theta_{2}/\tan\theta_{1}=\mu_{2}/\mu_{1}##
Note...
I agree with what you've said. I said what I did because I don't think many people are aware that the reason DC circuits work/behave as they do is surface charge on wires and interfaces. That is purely an electrostatics problem, but then of course there is also a magnetic field since ##\vec...
DC circuits in "equilibrium" so to speak (meaning a steady current) can be described using electrostatics. See, for example, J. A. Hernandes and A. K. T. Assis, Electric potential for a resistive toroidal conductor carrying a steady azimuthal current. Griffiths problem 7.42 is also a DC...