A place for discussions and planning for the Classical Electrodynamics Spring 2024 course
Questions about integrating cartesian unit vectors over spherical coordinates.
When integrating a unit vector like \hat{x} over d\phi , or any other coordinate system, how does \hat{x} being a function of \phi influence this? I know that if I had a volume element I could use the jacobian to translate between the spherical and cartesian volume elements, but how would I isolate just one part of that for one integral over a cartesian unit vector? Part of me thinks that it could be as simple as just multiplying \hat{x} by the range we are integrating it over because it is effectively like sweeping the circle around the xy plane if the bounds are 0 to 2\pi, but the fact that this is a vector and not a scalar makes me think otherwise.
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\hat{x}, \hat{y}, and \hat{z} are constants with respect to \phi and \theta, so you can just pull those out of the integral. only \hat{s}, \hat{\phi}, \hat{r}, and \hat{\theta} depend on \phi and/or \theta.
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Exactly, changing \phi or \theta will not change where \hat x is pointing at (and its magnitude is always fixed at |\hat x|=1). On the other hand, \hat r or \hat \theta or \hat \phi will change when you change the angles.
Here goes a repository with a first guided example on how to run jupyter notebooks in code spaces:
In the README file there is a link to a video recorded by Kyle and me on how to go through it too:
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some other options for running Python:
see also: Free Download | Anaconda
and: https://colab.research.google.com/
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Dear PHY 841 Students,
The course HW help sessions with me are:
Tue 15:00-17:00 (FRIB 1309)
Thu after colloquium(16:30ish)-18:00 (BPS 1415 requested)
Pablo’s help desk times are (see ASCSN for locations+changes to dates/times):
Wed 14:30-16:00
Fri 15:30-17:00
Best,
-Jaideep
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Hey friends!
I have an unexpected meeting from 4 to 5 pm on Friday Jan 19, so I will partition the Help desk office hour to be 3:30 - 4:00 on Zoom (email me), and I’ll swing by at 5:00 to the graduate student lounge to help anyone who is still there.
See you tomorrow (Wednesday) during normal hours at 2:30 pm!
Pablo
P.S. Be sure to check the general help desk announcements section: Spring 2024 Help Desk Annoucements - #4 by pablo
which is where I usually announce these things. I added this here because most Electrodynamics students are only checking this part of the forum 
Question on HW 02 Problem 3.6, 3.7.
I intuitively think that the integrals for the E-field are 0 on the axis of symmetry. However, the z-component integrals can’t be evaluated directly since \int_{-\infty} ^\infty \frac{z \hat{z}}{z^3} dz is undefined. I would appreciate some guidance on where to proceed from here.
As far as I’m aware the denominator/magnitude in your equation should be the magnitude of the separation vector, which for z should have a z-z’ term. What I have for my separation vector is pretty much what we get from ICP2 \vec{r_{sep}}=(x-s'\cos{\phi '})\hat{x} + (y-s'\sin{\phi '})\hat{y} +(z-z')\hat{z}. Taking the magnitude and centering it on the z axis should simplify some terms down.
Is the potential outside the sphere with the setup in problem 3 zero?