I understand this logically, as because as the sphere condenses towards r=0, only the delta functions would remain at the origin.
However, I normalized by the jacobian as such:
-δ(x)δ(y)δ(z) = δ(r)/(r2sin[θ])
And then integrated:
∫∫∫-[δ(r')/(r'2sin[θ])]r'2sin[θ] dr' dθ d∅...
Thanks TSny, I really appreciate the help.
That makes more sense. In "There is no angular dependence in the function, so the gradient will be simple in spherical coordinates," does this refer to a lack of angular dependence in the differential volume dV, or the function in question, ψ...
Homework Statement
By integrating (2-55), over a small volume containing the origin, substituting ψ = Ce-jβr/r, and letting r approach zero, show that C = 1/4π, thus proving (2-58).
Homework Equations
(2-55): ∇2ψ + β2ψ = -δ(x)δ(y)δ(z)
(2-58): ψ = e-jβr/(4πr)
The Attempt at a...
No takers? I understand this is a bit complicated and I haven't found anything on the internet that I've found helpful (or potentially have understood to be). Again, any help is appreciated.
If you notice, there are two rods: one connects to one set of plates (the light ones), and the second rod to the other (the dark ones). As these represent polarities, thus you can see that all the negative terminals and all the positive terminals are linked together, thus they're in parallel.
Seems right to me. It would be more complicated if they asked you to form an equation giving the capacitance based on an angle of rotation (and therefore variable overlap), but beyond that, I believe this is the correct approach.
Homework Statement
By integrating (2-55), over a small volume containing the origin, substituting ψ = Ce-jβr/r, and letting r approach zero, show that C = 1/4π, thus proving (2-58).
Homework Equations
(2-55): ∇2ψ + β2ψ = -δ(x)δ(y)δ(z)
(2-58): ψ = e-jβr/(4πr)
The Attempt at a...
The prof just sent an email that a value of current may not be sensibly calculated.
Thus, thank you kindly for your answer which appears to be correct!
Thanks for helping out an ignorant EE :)
Could you explain the charge/current density thing to me, namely where the delta-dirac functions come in?
Nevermind, I finally understand this part, thank you. What about above with the finding for current?
This question doesn't seem to be worth much and it's an EE class versus physics so I figure the answer has to be much simpler. Regardless, I did find something of note:
http://www.physics.sfsu.edu/~lea/courses/ugrad/460notes4.PDF
On page 7 it talks about moving point charges, and the other...
Alternatively, what if you consider the area dS to be δ(x)δ(y)?
i.e., you could treat the path the charge is on as an infinitely thin wire? Then the charge would be oscillating in it, which is what AC current is anyway. I mean realistically you could do that to a wire anyway, choose a...
Perhaps Biot-Savart? Would that be applicable to help in some way?
Alternatively, since v is in units of m/s, and q is in C, qv would produce units of Cm/s.
Given that A is the total amplitude of its motion, and therefore in m, would something like I = qv/A [= qωsin(ωt)] be closer or reasonable?
I'm currently in an antennas class, and while my EM is fairly strong, it's been a long time since I've done very basic electromagnetics like this question asks, so I can't clearly remember the specific details and physics properties. Any help is appreciated.
Homework Statement
We have...