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 'Inducing EMF Through a Coil: Understanding Flux'

Thread 'Inducing EMF Through a Coil: Understanding Flux'

Thank you for reading my post. I can understand why a change in magnetic flux through a conducting surface would induce an emf, but how does this work when inducing an emf through a coil? How does the flux through the empty space between the wires have an effect on the electrons in the wire itself? In the image below is a coil with a magnetic field going through the space between the wires but not necessarily through the wires themselves. Thank you.
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Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)'

Thread 'Griffith, Electrodynamics, 4th Edition, Example 4.8. (Second part)'

I am reading the Griffith, Electrodynamics book, 4th edition, Example 4.8. I want to understand some issues more correctly. It's a little bit difficult to understand now. > Example 4.8. Suppose the entire region below the plane ##z=0## in Fig. 4.28 is filled with uniform linear dielectric material of susceptibility ##\chi_e##. Calculate the force on a point charge ##q## situated a distance ##d## above the origin. In the page 196, in the first paragraph, the author argues as follows ...
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