Really challenging electric field problems

AI Thread Summary
The discussion focuses on the challenges of preparing for an upcoming open book test on electric fields, including Gaussian Law, capacitance, and circuits. The student expresses concern that the professor's decision to allow an open book format suggests the test will feature particularly difficult problems. Previous tough questions have involved complex integrations over continuous charge distributions. Participants are invited to share their experiences with challenging electric field problems. The thread highlights the anxiety surrounding the test's difficulty level.
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Ok, I'm studying electric fields this semester, covering Gaussian Law, capacitance, dielectric circuits and dc circuits.

Test coming up this thursday- open book. Which really bothers me alot. Judging from the standard of papers thus far, if the prof is allowing open book test, that can only mean his problems in mind are going to be insanely crazy. We can refer to all our textbook examples, tutorial material and study guides. The tougher questions so far usually involve integration over a continuous distribution of variables (charges or capacitance or whatever).

Just curious, what're the toughest, most insane questions any of you have come across so far?
 
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Thread 'Maxwell stress tensor'

This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
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Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'

Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
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