Cylindrical Capacitors Questions

In summary: The electric field between the conductors is inversely proportional to the length of the cylinder and directly proportional to the charge on the inner conductor. It is not dependent on the position within the cylinder. In summary, the electric field between the two conductors is given by E=Q/(2πε_0aL). The electric potential difference between the two conductors is given by V=Q/(2πε_0a)(ln(b/a)). The capacitance of the device is equal to ln(b/a)/(2πε_0a).
  • #1
apphysicsgirl
10
0

Homework Statement


An isolated cylindrical capacitor consists of two concentric conducting cylinders of length L and radii a and b. The inner and outer conductors carry +Q and -Q, respectively.
a. Determine the electric field between the conductors.
b. Determine the electric potential difference between the two conductors.
c. What is the capacitance of this device?

Homework Equations


V=[tex]\int[/tex]E dL
[tex]\oint[/tex]E dA=Q/Epsilon
C=Q/V

The Attempt at a Solution


a. I got as my answer E=Q/(2[tex]\pi[/tex]Epsilon not (aL))
b. I used the integral with V and got Q/(2[tex]\pi[/tex]Epsilon not (a) (ln(b/a))
c. I plugged my answer from b into C=Q/V and got ln(b/a)/(2[tex]\pi[/tex]Epsilon not (a))


I am not sure if I did any of these right...
 
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  • #2
apphysicsgirl said:

The Attempt at a Solution


a. I got as my answer E=Q/(2[tex]\pi[/tex]Epsilon not (aL))
b. I used the integral with V and got Q/(2[tex]\pi[/tex]Epsilon not (a) (ln(b/a))
c. I plugged my answer from b into C=Q/V and got ln(b/a)/(2[tex]\pi[/tex]Epsilon not (a))


I am not sure if I did any of these right...

Is the electric field independent of position?

ehild
 

What is a cylindrical capacitor?

A cylindrical capacitor is a type of electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by an insulating material, with a cylindrical shape.

How does a cylindrical capacitor work?

A cylindrical capacitor works by storing electrical charge on its conductive plates. When a voltage is applied, one plate becomes positively charged while the other becomes negatively charged. The insulating material between the plates prevents the charges from moving and creates an electric field.

What are the applications of cylindrical capacitors?

Cylindrical capacitors are used in various electronic devices, such as radios, televisions, and computers. They are also commonly used in power supply circuits, as well as in energy storage systems.

What is the capacitance of a cylindrical capacitor?

The capacitance of a cylindrical capacitor depends on its physical dimensions, such as the surface area of the plates and the distance between them. It is measured in units of farads (F).

How can I calculate the capacitance of a cylindrical capacitor?

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

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