# Finding the electric potential above a charged metal toroid (electrostatic lens)

Callumnc1
Homework Statement:
Relevant Equations:
For A.1 of this problem,

The solution is

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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Callumnc1
Callumnc1

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

Many thanks!

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