Potential of hollow open ended cylinder

In summary, the conversation discusses finding the difference in potential between a point on the axis at one end of a hollow circular cylinder with a uniform charge distribution and the midpoint of the axis. The suggested approach is to use the potential on the axis of a circular ring of charge and then use integration to calculate the potential for the entire cylinder. The formula for the potential on the axis of a circular ring of charge is mentioned as a starting point for the solution.
  • #1
FS98
105
4

Homework Statement



A hollow circular cylinder, of radius a and length b, with open ends, has a total charge Q uniformly distributed over its surface. What is the difference in potential between a point on the axis at one end and the midpoint of the axis? Show by sketching some field lines how you think the field of this thing ought to look.

Homework Equations

The Attempt at a Solution


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I’m pretty sure I have to get the potential at one end of the open ended cylinder and then subtract the potential at the middle. I think the potential at the center is 0 because of symmerty, so the only think I have to find is the potential at one end. I’m not sure what equation to use for this though.
 
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  • #2
Perhaps you should start with the potential on the axis of a circular ring of charge, then think integration to "build up" your cylinder :wink: You've probably seen the result for the ring of charge, either in class or in your study materials. What is the formula?
 

Related to Potential of hollow open ended cylinder

1. What is a hollow open ended cylinder?

A hollow open ended cylinder is a cylindrical shape with open ends, meaning there is no material closing off the top or bottom of the cylinder. It is essentially a tube with a hollow interior.

2. What are the potential uses for a hollow open ended cylinder?

There are many potential uses for a hollow open ended cylinder, including as a container or storage vessel, as a structural element in buildings or bridges, and as a component in machinery or equipment. It can also be used in scientific experiments and demonstrations.

3. How is the potential of a hollow open ended cylinder determined?

The potential of a hollow open ended cylinder depends on several factors such as its dimensions, material, and intended use. The potential can be calculated using mathematical equations based on the specific properties of the cylinder.

4. What advantages does a hollow open ended cylinder have over a solid cylinder?

A hollow open ended cylinder is often lighter and more cost-effective than a solid cylinder of the same size and material. It also allows for more flexibility in terms of customization and use, as the open ends can be used for various purposes.

5. Are there any limitations to the potential of a hollow open ended cylinder?

Like any other object, a hollow open ended cylinder has its limitations. These can include factors such as the material strength, structural stability, and maximum load capacity. These limitations should be taken into consideration when designing and using a hollow open ended cylinder.

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