Need help about charged ring

Charged ring

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.

Replies

  • Ramani Aswath
    Ramani Aswath
    Aruwin,
    The picture does not open.
  • Aruwin
    Aruwin
    A.V.Ramani
    Aruwin,
    The picture does not open.
    Here, click on this link. Or copy and paste it.
    potential due to ring charge | elly.ppp2013 | Flickr
  • Harshad Italiya
    Harshad Italiya
    Aruwin
    Here, click on this link. Or copy and paste it.
    potential due to ring charge | elly.ppp2013 | Flickr
    I fixed your first post with Image.
  • Ramani Aswath
    Ramani Aswath
    Dear Aruwin,
    This is not my area at all. Probably these links may help you.
    #-Link-Snipped-#


    #-Link-Snipped-#

    #-Link-Snipped-#
    #-Link-Snipped-#
  • Aruwin
    Aruwin
    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.
  • Ramani Aswath
    Ramani Aswath
    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.
  • Aruwin
    Aruwin
    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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