# Mutual inductance in concentric cylinders

• derek88
Expert SummarizerIn summary, the conversation discusses the mutual inductance between two concentric conducting cylinders and how it affects their impedance. The mutual inductance is determined by equations that include the term LN(R2/R1) and it contributes to the impedance of both cylinders. The forum member's understanding is mostly correct, but the expert clarifies that the equations for mutual inductance should include the LN(R2/R1) term in both cases.
derek88
Friends:

I have been thinking about this question for a while, so I hope you can help! Here it is:

Lets say you have two concentric, conducting cylinders.

The outer cylinder ("Cylinder 2") has the following properties: radius R2, carries a current of I2, relative magnetic permeability mu2, impedance of Z2 = R2 + jwL2.

The inner cylinder ("Cylinder 1") has the following properties: radius R1, carries a current of I1 (in the same direction as I2), relative magnetic permeability mu1, impedance of Z1 = R1 + jwL1.

My question is: how does the mutual inductance between these cylinders increase their impedance?

My guess is the following:

"Cylinder 1" creates a magnetic field B = (mu0)(mu1)(I1)/(2*pi*R1)
This creates a mutual inductance on "Cylinder 2". The mutual inductance created on "Cylinder 2" is M21 = [(mu0)(mu1)(I1)/(2*pi*R1)]*LN(R2/R1).
Thus the impedance of "Cylinder 2" increases to Z2 = R2 + jwL2 + jwM21.

"Cylinder 2" creates a magnetic field B = (mu0)(mu2)(I2)/(2*pi*R2). However, this field exists only outside the cylinder. Inside the cylinder, the magnetic field is 0. Therefore, the mutual inductance created on "Cylinder 1" by "Cylinder 2" is M12 = 0.
Thus the impedance of "Cylinder 1" remains unchanged at Z1 = R1 + jwL1.

Please let me know if this is correct or if I'm terribly mistaken! Thank you kindly!

Thank you for your question about the mutual inductance between two concentric conducting cylinders. Your understanding of the concept is mostly correct, but I would like to clarify a few points for you.

First, you are correct in saying that "Cylinder 1" creates a magnetic field that induces a mutual inductance on "Cylinder 2". This mutual inductance is determined by the equation M21 = (mu0)(mu1)(I1)(LN(R2/R1))/2pi. However, this mutual inductance also contributes to the impedance of "Cylinder 1" because it is affected by the magnetic field created by "Cylinder 2". Therefore, the impedance of "Cylinder 1" will also increase to Z1 = R1 + jwL1 + jwM21.

Additionally, you mentioned that the magnetic field created by "Cylinder 2" is only present outside the cylinder. This is true, but it still contributes to the mutual inductance on "Cylinder 1". The equation for this mutual inductance is M12 = (mu0)(mu2)(I2)(LN(R2/R1))/2pi, and it does affect the impedance of "Cylinder 1" as well.

In summary, the mutual inductance between the two cylinders will contribute to the impedance of both cylinders, and the equations for mutual inductance in both cases should include the term LN(R2/R1). I hope this helps clarify your understanding. Let me know if you have any further questions.

## 1. What is mutual inductance in concentric cylinders?

Mutual inductance in concentric cylinders is a phenomenon that occurs when two or more cylinders with conductive material are placed inside each other. The changing magnetic field in one cylinder induces an electromotive force (EMF) in the other cylinder, causing a flow of current.

## 2. How is mutual inductance calculated in concentric cylinders?

Mutual inductance in concentric cylinders can be calculated using the formula M = μN1N2A/l, where μ is the permeability of the material, N1 and N2 are the number of turns in the respective cylinders, A is the cross-sectional area, and l is the length of the cylinders.

## 3. What factors affect mutual inductance in concentric cylinders?

The factors that affect mutual inductance in concentric cylinders include the distance between the cylinders, the number of turns in each cylinder, the permeability of the material, and the cross-sectional area of the cylinders.

## 4. What are the applications of mutual inductance in concentric cylinders?

Mutual inductance in concentric cylinders has various applications, including in electrical transformers, generators, and motors. It is also used in wireless power transfer and inductive coupling in electronic devices.

## 5. How does mutual inductance in concentric cylinders differ from self-inductance?

Self-inductance refers to the phenomenon of induction in a single coil or conductor, while mutual inductance occurs between two or more coils or conductors. In mutual inductance, the changing magnetic field in one coil induces an EMF in the other coil, whereas in self-inductance, the changing current in the same coil induces an EMF in the same coil.

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