Capacitance of three coaxial metal tubes

In summary: The capacitance per unit length of three long coaxial metal tubes, with radii a < b < c. A wire connects the innermost and outermost tubes (radii a and c). The Attempt at a SolutionIn summary, the capacitance per unit length is two times the potential difference between the inner and middle cylinder.
  • #1
boardbox
16
0

Homework Statement



Find the capacitance per unit length of three long coaxial metal tubes, with radii
a < b < c . A wire connects the innermost and outermost tubes (radii a and c).

Homework Equations





The Attempt at a Solution



I'm a little confused as to how I should set this up. What confused me is the wire that runs between the innermost and outermost tube. My thought is that it just makes the two tubes one big conductor. If that's the case and I put some charge on the conductor, how does it get distributed? Could I just put a charge on it and say the charge on the innermost tube is the area of the innertube over the area of the whole conductor times the charge?
 
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  • #2
boardbox said:
Could I just put a charge on it and say the charge on the innermost tube is the area of the innertube over the area of the whole conductor times the charge?

I don't think you can assume that. However, if the two cylinders are connected by a conducting wire, you can say that they are equipotentials.
 
  • #3
Alright well let me think this out for a second.

What I'm after is the potential from c to a, after that the problem is simple. That's going to be V(c) - V(a). Well V changes, so taking two steps V(c) - V(b) + V(b) - V(a). If V(c) = V(a) then I get zero potential. That seems a little silly to me, also means I'm dividing by zero in the next step, so I don't think that's right.

Here's another thought and this strikes me as a bit less silly. Say I have some charge on the innermost cylinder and some other charge on the middle cylinder. I could find the potential difference between the two. Now I know the outermost cylinder has the same potential at the innermost one, which means that the potential difference between it and the middle cylinder is the same as the difference between the middle cylinder and inner cylinder. So the potential of the set is just two times the potential between the inner and middle cylinder.
 
  • #4
boardbox said:
What I'm after is the potential from c to a, after that the problem is simple.

Why do you say that? What is the applicable definition of capacitance here?
 

FAQ: Capacitance of three coaxial metal tubes

1. What is capacitance?

Capacitance is the ability of a conductor to store electric charge. It is measured in farads (F) and is dependent on the geometry of the conductor and the surrounding medium.

2. How is capacitance calculated for three coaxial metal tubes?

The capacitance of three coaxial metal tubes can be calculated using the formula C = (2πε0εr/ln(b/a)) + (2πε0εr/ln(c/b)), where ε0 is the permittivity of free space, εr is the relative permittivity of the surrounding medium, and a, b, and c represent the radii of the inner, middle, and outer tubes, respectively.

3. How does the capacitance change with the distance between the tubes?

The capacitance between three coaxial metal tubes is inversely proportional to the distance between the tubes. As the distance between the tubes increases, the capacitance decreases.

4. What factors affect the capacitance of three coaxial metal tubes?

The capacitance of three coaxial metal tubes is affected by the radii of the tubes, the distance between the tubes, and the relative permittivity of the surrounding medium. It is also influenced by the dielectric material between the tubes, if present.

5. Why is capacitance important in electrical circuits?

Capacitance plays a crucial role in electrical circuits as it allows for the storage and release of electrical energy. It is used in various devices such as filters, oscillators, and power supplies. Capacitance also affects the behavior and performance of electrical circuits, making it an important factor to consider in circuit design.

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