Electrodynamics i need some help

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A user seeks assistance with a physics problem involving a charged cylinder and two external charges, specifically how to calculate the equilibrium distance of the charges from the cylinder using the method of images. The cylinder has a charge of +1, while the external charges are both -1/2 and positioned equidistantly from the cylinder's center. The user has made modifications to the original problem and provided additional details in a document. The discussion focuses on applying the method of images to solve the problem. Clarification and guidance on the calculations are requested.
ggups
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Hi,
This is my first post, am excited to be here. Cutting to the chase here, i have a question that has been bothering me for a while.
The problem is there is a charged cylinder with charge say +1, and i have to charges outside say at a distance 'd' from the center of the cylinder such that they lie in a single staright line passing thorugh the center. Now i wish to find the equillibrum distance of the charges from the cylinder(by symmetry both are equsidistant from the center of the cylinder). Also the charges are -1/2. How can i calculate the distance using method of images.


thanks
ggups
 
Last edited:
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some modification

The previous problem that i gave has some modification. I have written some details in the document.
Thanks
ggups
 

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Thread 'How to picture the vector potential?'

Susskind (in The Theoretical Minimum, volume 1, pages 203-205) writes the Lagrangian for the magnetic field as ##L=\frac m 2(\dot x^2+\dot y^2 + \dot z^2)+ \frac e c (\dot x A_x +\dot y A_y +\dot z A_z)## and then calculates ##\dot p_x =ma_x + \frac e c \frac d {dt} A_x=ma_x + \frac e c(\frac {\partial A_x} {\partial x}\dot x + \frac {\partial A_x} {\partial y}\dot y + \frac {\partial A_x} {\partial z}\dot z)##. I have problems with the last step. I might have written ##\frac {dA_x} {dt}...
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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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