# Potential of a cylinder with uniform charge

• risendemon
In summary, the conversation discusses finding the potential of a cylinder with uniform volume charge sigma, radius r, and length L. The approach suggested is to find the electric field resulting from a disk of charge and integrate it to find the potential. The challenge is setting up the integration due to varying theta and distance from the disk to the point of reference. The conversation also includes a link to a picture of the problem and a request for help with posting equations and pictures on the thread. The conversation ends with the poster sharing their own solution for setting up the integral and asking for confirmation.

#### risendemon

Hi, I'm new here, and I'm sure you will be hearing from me often in here

anyway, my question is in regards to finding the potential of a cyllinder, with uniform volume charge sigma, radius r, and length L. In this case, I need to find the potential along the axis of the cylinder, but outside of the charge distribution.

I have an idea how to do it, let me know if I'm on the right track. I decided the best way to go about doing this is to find the electric field resulting on the point of reference from a disk of charge, with surface charge d(sigma), and building the cylinder out of an infinite amount of disks from distance z to distance z+L- then using the electric field to find the electric potential. I found the electric field resulting from the disk of charge, but am having trouble setting up the integration to find the field due to the volume, because theta varies, and so does the distance from the disk and the point of reference. Any help would be appreciated. Does anyone know of an easier way to tackle this problem?

here's a picture of the problem to make things easier:
http://i43.photobucket.com/albums/e394/risendemonx/potentialcylinder.jpg [Broken]

oh, and one last thing: since I'm new here, can anyone show me how to post equations and pictures directly to the thread? thanks a bunch!

Last edited by a moderator:
actually, I think I figured out an easier way to set up the integral, could someone check to make sure I didn't mess up somewhere?

http://i43.photobucket.com/albums/e394/risendemonx/potentialcylinder2.jpg [Broken]

thanks!

Last edited by a moderator:

## 1. What is the equation for the potential of a cylinder with uniform charge?

The equation for the potential of a cylinder with uniform charge is V = k * λ / r, where V is the potential, k is the Coulomb constant, λ is the linear charge density, and r is the distance from the center of the cylinder.

## 2. How is the potential of a cylinder with uniform charge different from that of a point charge?

The potential of a cylinder with uniform charge is different from that of a point charge because it takes into account the distributed charge along the length of the cylinder, whereas the potential of a point charge is solely dependent on the distance from the charge.

## 3. Can the potential of a cylinder with uniform charge be negative?

Yes, the potential of a cylinder with uniform charge can be negative. This occurs when the distance from the center of the cylinder is greater than the length of the cylinder, resulting in a negative potential value.

## 4. How does the potential of a cylinder with uniform charge change with distance?

The potential of a cylinder with uniform charge follows an inverse relationship with distance. As the distance from the center of the cylinder increases, the potential decreases.

## 5. Is the potential of a cylinder with uniform charge affected by the radius of the cylinder?

Yes, the potential of a cylinder with uniform charge is affected by the radius of the cylinder. As the radius increases, the potential decreases, as seen in the equation V = k * λ / r. Additionally, a larger radius results in a larger surface area for the charge to be distributed, resulting in a lower potential.