Calculating Electric Potential for a Non-Negligible Thickness Toroid

AI Thread Summary
The discussion revolves around calculating the electric potential of a toroid with a non-negligible thickness. There is confusion regarding the linear charge density, specifically why it is expressed as λ = q/(2πR) despite the toroid's width of 2a. Participants highlight that the toroid's larger area implies a potentially lower linear charge density. The challenge of determining the charge distribution for a metallic toroid is acknowledged as a significant complexity in the calculations. Overall, the conversation emphasizes the need for a revised approach to account for the toroid's thickness in electric potential calculations.
member 731016
Homework Statement
Please see below
Relevant Equations
Please see below
For A.1 of this problem,
1675405830601.png

The solution is
1675399497646.png

However, I have a doubt about the linear charge density ##\lambda##.

I don't understand how ##\lambda = \frac {q}{2\pi R} ## since this is not a thin ring, but has a non-negligible width of ##2a##

I think that the toroid has a larger area than thin circle with a circumference ##2\pi R## so linear charge density should be less than that expression.

EDIT: How would we calculate the electric potential if the thickness was not neglected?

Many thanks !

Problem from:
https://www.ipho2021.lt/uplfiles/Th2.pdf
https://www.ipho2021.lt/uplfiles/Th2-Solution.pdf
 

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1675414550671.png
 
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BvU said:
Thank you for your reply @BvU!

However, how would we calculate the electric potential if the thickness was not neglected?

Many thanks!
 
Callumnc1 said:
Thank you for your reply @BvU!

However, how would we calculate the electric potential if the thickness was not neglected?

Many thanks!
Since it is metallic, your first challenge would be to figure out the charge distribution. Good luck with that.
 
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haruspex said:
Since it is metallic, your first challenge would be to figure out the charge distribution. Good luck with that.
Thank you for your reply @haruspex! Yeah that seems hard!
 
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