I Electric field of ring at any point

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Calculating the electric field due to a uniformly charged ring at points not on the perpendicular axis involves complex integrals. Users have noted that applying Coulomb's law and the divergence of electric potential often leads to complicated calculations. The integral for this scenario does not yield a simple closed-form expression, which can be a source of frustration. It's essential to approach the problem with an understanding of the complexities involved. The discussion emphasizes the challenges of finding a straightforward solution in this context.
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How to calculate the field due to a uniformly charged ring at a point not on the perpendicular axis of the plane of the ring
I have tried using coulomb's law and divergennce of the electric potential but I always stumble with a complicated integeral
 
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That’s because the corresponding integral is complicated. You should worry if you found a simple closed form expression.
 
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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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