Need help about charged ring

@aruwin-WQ7eeu • Oct 26, 2024

Oct 26, 2024

2.3K

The picture above shows the potential due to ring charge. (you need to right click on the picture box and open on new tab)
Please show the full steps of deriving the equation of electrical potential above.

NOTE:
The electric potential of the revolving symmetrical ring electric charge related to the axis z as depicted in the diagram 5.3, is also called a charged coil or a charged ring in the electromagnetism books, but most of the time, it gives an infinite series of equation that uses Legendre function. It is commonplace to use complete circle integral function in the charge simulation method. If the position (height) of ring electric charge is Z, the radius is R, and the charge density is λ, the electric potential of the point P will be as represented in the next equation.

In the equation, l is the distance between the part of the ring charge dθ and P.

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Ramani Aswath

@ramani-VR4O43 • Jun 16, 2014

Aruwin,
The picture does not open.
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Aruwin

@aruwin-WQ7eeu • Jun 16, 2014

A.V.Ramani
Aruwin,
The picture does not open.
Here, click on this link. Or copy and paste it.
<a href="https://www.flickr.com/photos/98820721@N04/14436573831/lightbox/" target="_blank" rel="nofollow noopener noreferrer">potential due to ring charge | elly.ppp2013 | Flickr</a>

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Harshad Italiya

@harshad-ukH5ww • Jun 16, 2014

Aruwin
Here, click on this link. Or copy and paste it.
<a href="https://www.flickr.com/photos/98820721@N04/14436573831/lightbox/" target="_blank" rel="nofollow noopener noreferrer">potential due to ring charge | elly.ppp2013 | Flickr</a>
I fixed your first post with Image.

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Ramani Aswath

@ramani-VR4O43 • Jun 16, 2014

Dear Aruwin,
This is not my area at all. Probably these links may help you.
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Aruwin

@aruwin-WQ7eeu • Jun 17, 2014

A.V.Ramani
Dear Aruwin,
This is not my area at all. Probably these links may help you.
#-Link-Snipped-#

#-Link-Snipped-#

#-Link-Snipped-#
#-Link-Snipped-#
Thanks but this is different from the question because the coordinate P is not located along the z-axis as shown in the video.

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Ramani Aswath

@ramani-VR4O43 • Jun 17, 2014

If P is on the same plane as the ring, the situation is more complex.
l becomes a variable. The ring will now be a line as seen from P but with the charge varying from the point on the circumference on the radius passing through P (at distance l) till the tangent to the ring from P. I think that the charge at any point will be the actual charge density on the ring element multiplied by cos(theta), where theta will be the angle of the line joining that point with P and the radius through P.

The included angle between the two tangents to the ring will become the limits for the integral.
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Aruwin

@aruwin-WQ7eeu • Jun 17, 2014

A.V.Ramani
If P is on the same plane as the ring, the situation is more complex.
l becomes a variable. The ring will now be a line as seen from P but with the charge varying from the point on the circumference on the radius passing through P (at distance l) till the tangent to the ring from P. I think that the charge at any point will be the actual charge density on the ring element multiplied by cos(theta), where theta will be the angle of the line joining that point with P and the radius through P.

The included angle between the two tangents to the ring will become the limits for the integral.
Could you illustrate it please? I can't imagine it in my head 😔
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