Cylindrical Capacitor

In summary, the speaker's professor has assigned a problem regarding finding the radius of a cylinder within a cylindrical capacitor with radii a and b. The formula for capacitance should be used, but the speaker is struggling with the q variable in the equation for electric potential energy. The professor wants the speaker to find the radius of a cylinder that contains half of the stored electric potential energy, and there is a picture provided showing a cross section of the cylinder. The speaker has attempted to use various equations and calculations, including the Integral used to derive electric potential energy, but is still unable to solve the problem.
  • #1
rey242
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Homework Statement


Hey guys, My prof asked us to find the radius of a cylinder within a cylindrical capacitor with 2 radii a and b. I know we use the Capacitance formula for a cylinder but I can't seem to get pass the q that shows up when I plug it into the 1/2 c*V^2

EDIT: He wants us to find a cylinder's radius that contains half the stored electric potential energy.
 
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  • #2
I'm afraid you'll need to be a lot more specific than that. Can you give us the full question (word-for-word), plus all of the equations you used and all of the calculations you tried?
 
  • #3
Oh I'm sorry, I forgot to add something. He wants us to find a cylinder's radius that contains half the stored electric potential energy.

Yea there's a picture he showed us, a long cylindrical capacitor. The picture shows a cross section of the cylinder. The smaller cylinder within the bigger one has a radius a and the bigger one has a radius b. The radius of an arbitrary cylindrical Gaussian surface between a and b is r.

I tried to use C= 2pi E0 (L/ ln(b/a)) for the capacitance and use it with both forms of Electric Potential energy equation(q^2/r and 1/2cV^2). But I get stuck on the charge q variable. and I even tried to use the Integral used to derive Elec. Potent. Eng. but I can't really figure that out what to do with that.
 
  • #4
Even though the homework assignment passed, I would still like an answer to this. :)
 

Related to Cylindrical Capacitor

1. What is a cylindrical capacitor?

A cylindrical capacitor is a type of electronic component that is used to store and release electrical energy. It consists of two conductive plates, usually made of metal, separated by an insulating material, known as a dielectric. The two plates are cylindrical in shape, with one plate inside the other.

2. How does a cylindrical capacitor work?

A cylindrical capacitor works by storing electrical energy between its two plates. When a voltage is applied across the plates, an electric field is created between them. The amount of energy that can be stored depends on the capacitance of the capacitor, which is determined by the distance between the plates and the type of dielectric material used.

3. What are the applications of a cylindrical capacitor?

Cylindrical capacitors are used in a variety of electronic devices, including power supplies, electric motors, and audio equipment. They are also commonly used in radio frequency circuits, such as in antennas and transmitters.

4. How is the capacitance of a cylindrical capacitor calculated?

The capacitance of a cylindrical capacitor can be calculated using the formula C = (2πεrL) / ln(b/a), where C is the capacitance, ε is the permittivity of the dielectric material, r is the radius of the inner plate, L is the length of the capacitor, and a and b are the radii of the inner and outer plates, respectively.

5. What are the advantages and disadvantages of a cylindrical capacitor?

One advantage of a cylindrical capacitor is that it has a large surface area, which allows for a higher capacitance compared to other capacitor shapes. However, it also has a larger physical size, making it less suitable for applications with limited space. Additionally, cylindrical capacitors can be more expensive to manufacture compared to other types of capacitors.

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