Calculating Electric Potential for a Non-Negligible Thickness Toroid

In summary, the conversation discusses a problem involving calculating the electric potential in a toroid with a non-negligible thickness. The solution is given, but there is a doubt about the linear charge density and its relation to the toroid's dimensions. The conversation ends with a question about how to calculate the electric potential with a non-neglected thickness.
  • #1
ChiralSuperfields
1,171
132
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
 

Attachments

  • 1675399479240.png
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Last edited:
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  • #2
1675414550671.png
 
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Likes ChiralSuperfields
  • #3
BvU said:
Thank you for your reply @BvU!

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

Many thanks!
 
  • #4
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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  • #5
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!
 

1. How do you calculate the electric potential for a non-negligible thickness toroid?

To calculate the electric potential for a non-negligible thickness toroid, you can use the formula V = (kQ)/(R) where V is the electric potential, k is the Coulomb's constant, Q is the charge of the toroid, and R is the distance from the center of the toroid to the point of interest.

2. What is a non-negligible thickness toroid?

A non-negligible thickness toroid is a toroid with a thickness that is significant enough to affect the calculation of electric potential. This means that the thickness cannot be ignored and must be taken into account when calculating the electric potential.

3. What is the difference between a non-negligible thickness toroid and a thin toroid?

The main difference between a non-negligible thickness toroid and a thin toroid is that the thickness of a non-negligible thickness toroid cannot be ignored in calculations, while the thickness of a thin toroid can be considered negligible and therefore does not significantly affect the calculation of electric potential.

4. How does the thickness of a toroid affect the calculation of electric potential?

The thickness of a toroid affects the calculation of electric potential by changing the distance from the center of the toroid to the point of interest. As the thickness increases, the distance also increases, resulting in a decrease in electric potential.

5. Can the electric potential for a non-negligible thickness toroid be negative?

Yes, the electric potential for a non-negligible thickness toroid can be negative. This can occur if the charge of the toroid is negative or if the distance from the center of the toroid to the point of interest is greater than the radius of the toroid.

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