Capacitance and Inductance of Thin Metal Ribbons

• ehrenfest
In summary, the conversation discusses the construction of a transmission line using two thin metal ribbons and the determination of capacitance and inductance per unit length. Part a) involves finding the capacitance per unit length, while part b) involves understanding the concept of inductance and determining its value per unit length. The confusion arises from the volume between the ribbons and the need to choose an appropriate area for calculating flux.
ehrenfest

Homework Statement

21. A certain transmission line is constructed from two thin metal “ribbons”, of width w, a very small distance w<<h apart. The current travels down one strip and back the other strip. In each case it spreads out uniformly over the surface of the ribbon.
a) Find the capacitance per unit length.
b) Find the inductance per unit length.

The Attempt at a Solution

Part a) is easy. I do not understand what part b) is asking. I can find the B-field between the ribbons. But I don't understand how inductance makes sense here. Inductance is defined by $\Phi = LI$. The magnetic flux $\Phi$ is the B-field per unit area. But here we have a volume not an area between the ribbons. I am so confused.

Right, there is a volume between the ribbons, but there are also areas. Flux is how much of the field travels through a certain area, so you need to pick which area makes sense. Just ask yourself what direction does the magnetic field point in, and should I look length wise or width wise?

1. What is capacitance?

Capacitance is a measure of the ability of a capacitor to store electrical energy in the form of an electric field. It is defined as the ratio of the electric charge stored on the capacitor to the potential difference between its plates.

2. What is inductance?

Inductance is a measure of the ability of a conductor to generate an electromotive force (EMF) when an electrical current is passed through it. It is defined as the ratio of the EMF generated to the rate of change of current.

3. How do thin metal ribbons affect capacitance and inductance?

Thin metal ribbons have a large surface area compared to their size, which increases their capacitance. They also have a low resistance, which decreases their inductance.

4. What factors affect the capacitance and inductance of thin metal ribbons?

The capacitance of thin metal ribbons is affected by the distance between the ribbons, the thickness and width of the ribbons, and the dielectric material between the ribbons. The inductance is affected by the shape, length, and material of the ribbons, as well as the frequency of the current passing through them.

5. How can we calculate the capacitance and inductance of thin metal ribbons?

The capacitance of thin metal ribbons can be calculated using the formula C = εA/d, where ε is the permittivity of the dielectric material, A is the area of the ribbons, and d is the distance between them. The inductance can be calculated using the formula L = μl/πr, where μ is the permeability of the material, l is the length of the ribbon, and r is the radius of the ribbon.

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