Use of potentials (electrodynamics, classical)

bman!!
Messages
26
Reaction score
0
hello, I've just gone through a derivation using the vector potential A, and using the equation derived (a wave equation) which arises from using the lorentz gauge, it is applied to the problem of a current sheet in the xy plane, located at z=0 with current in the x direction only. the current varies with time so we are looking for wave solutions propagating in the + and - z directions.

Ive attached the relevant page (its not long at all), and basically my problem is simply: i understand pretty much everything up until equation 6.46, however, i cannot for the life of me understand how he gets to 6.47.

i know its probably something really simple, probably like a nifty application of the chain rule, but Id appreciate if someone could point out the elephant to me becuase i really can't see it and its annoying the hell out of me.

cheers

(im sure the answer will make me feel like an Rtard)
 

Attachments

  • use of potentials-current sheet.JPG
    use of potentials-current sheet.JPG
    43.3 KB · Views: 450
Physics news on Phys.org
is the picture not working or something? its just a simple boundary (jump?) conditions problem. i say simple, I'm pretty terrible with jump conditions, so any help is really appreciated. this one step is driving me mad!
 
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
Back
Top