# What is Mutual inductance: Definition and 119 Discussions

Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the current, and follows any changes in current. From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors, a process known as electromagnetic induction. This induced voltage created by the changing current has the effect of opposing the change in current. This is stated by Lenz's law, and the voltage is called back EMF.
Inductance is defined as the ratio of the induced voltage to the rate of change of current causing it. It is a proportionality factor that depends on the geometry of circuit conductors and the magnetic permeability of nearby materials. An electronic component designed to add inductance to a circuit is called an inductor. It typically consists of a coil or helix of wire.
The term inductance was coined by Oliver Heaviside in 1886. It is customary to use the symbol

L

{\displaystyle L}
for inductance, in honour of the physicist Heinrich Lenz. In the SI system, the unit of inductance is the henry (H), which is the amount of inductance that causes a voltage of one volt, when the current is changing at a rate of one ampere per second. It is named for Joseph Henry, who discovered inductance independently of Faraday.

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1. ### I Mutual inductance of bifilar winding, vs transmission line parameter

Is there a relation between the mutual inductance across a pair of bifilar wound coils, and the inductance per meter of the same winding considered as a transmission line? I.e., can one calculate one from the other?
2. ### Current through ring in solenoid-ring system

The following is my solution to this problem; I would appreciate some feedback, especially on part (b), which I have found the most challenging. Thanks. (a) Using Ampere's Law I get ##B=\mu_0 n i_1## where ##i_1## is the current through the solenoid, and since ##\phi=Li_1##, where ##L## is the...
3. ### Engineering Mutual Inductance between two conductors

Hello hope everyone at PF are keeping well! Looking at this problem but don't know if I have oversimplified it and my final answer doesn't seem right? So I drew the equivalent circuit: Then went onto calculate: I1 = 1/(R1+RL1) = 0.01A ω = 2πf = 2π*109 rads-1 so then with Vi being the inducted...
4. ### Finding Inductance and Mutual Inductance

I am trying to solve for inductance through FEA simulation. I and doing eddy current simulations so I can have H field, B field, and current density available. I am also trying to find an equation for the equivalent inductance with multiple conductors. I know that for two conductors it is Leq...
5. ### Clarification about Mutual Inductance

emf = ##\frac {-N_{2} {d\phi}_{B2}} {dt}## ## M_{21} = \frac {{N_2}{\phi}_{B2}} {i_1}## are the equations This is the original position, now the coil 2 is moved so the axis is perpendicular. The flux ##{\phi}_{B2}## due to i1 is the amount of flux cutting the coil 2 due to change in current...
6. ### Accounting for mutual inductance in a Hartley Oscillator

Hi, I'm watching a video about Hartley oscillator and I'm in trouble with a simple assumption: as stated at minute 5:50 if the two coils ##L_1## and ##L_2## are wound on the same core then taking into account the mutual inductance M he gets: ##L^ {'} _1 = L_1 + M## ##L^ {'} _2 = L_2 + M##...
7. ### Mutual Inductance between a coil and a long straight wire

In the given question they have not provided the dimensions of the coil so I assumed it to be very close to the wire and having negligible dimensions compared to the wire . Then EMF induced in the coil due to the current in the wire comes out as M*a . Which when divided by resistance gives...
8. ### Mutual inductance between a very long, straight wire and a Semicircular loop

I think I have to assume a point like P in the semicircle. The point in terms of r and θ: P (r,θ). So the magnetic field at that point: B = µI/2π(R+rcosθ) . So the magnetic flux: Φ = ∫B.dA= µI/2π ∫∫ rdrdθ / R+rcosθ . Is this the correct solution?
9. ### A problem in mutual inductance

I have gotten my average induced emf to be 96 x 10^-3V using the formula, e=Nx(∆I)/t but the problem lies in calculating the inductances.
10. ### Does Mutual Inductance Affect Voltage in an Open Circuit?

Hi, so my question is basically: Does the mutual inductance from coil 1 show up in the voltage of coil 2 even if coil 2 is an open circuit? I would think that the answer is yes, as the Mutual inductance depends on the current passing through coil 1? However, the answer scheme seems to ignore...
11. ### Dot convention inductors in series: equation confusion

Homework Statement So I'm really confused with mutual inductors and dot convention. If your answer is going to be a link to any website I can assure you I read them all and that only left me more confused. So here are my questions: Homework Equations 3. The Attempt at a Solution [/B] ->...
12. ### Mutual inductance coefficient with so little info

Homework Statement I have the following circuit: The two inductors are connected in series are characterized by internal resistances R1 and R2 and self-inductances L11 and L22. The magnetic coupling factor between the inductors is k = 0.75. The inductors carry the same current i. What is the...
13. ### Mutual Inductance of Coaxial Tube and Coil

In my lab we are working with a Coaxial coil and stainless steel tube, and are aiming to find the mutual Inductance. I've done some looking around and have easily found the Inductance of a Coaxial cable, and for that of Coaxial coils, but am having trouble with a combination of the two. The...
14. ### Mutual Inductance Homework Help: Q4d Stuck, Need Advice

Homework Statement I have included the questions and circuits. I have used previous post to help but am still stuck Homework Equations included in files The Attempt at a Solution I have worked hard to get to the question 4d. I am stuk because using previous posts to help I do not know if I...
15. ### Mutual inductance and magnetic feild

hi, in this problem here there's 2 perpendicular coils but in solution there's an effect of mutual inductance why?
16. ### Mutual inductance of a coil inside a solenoid

Good day , i have an issue with the derivation of the mutual inductance of coil inside solenoid formula I1 is an alternating current which means that B is varying, and we know that the Flux 21 is equal to the integral of the dot product of B and A2 but as B is varying we CAN NOT take it out...
17. ### Mutual Inductance of two coaxial coils

Homework Statement Two coils of the same length and almost the same cross-section are put one inside the other. Find their mutual inductance if the self-inductances are and . Homework Equations 1) \phi_i=L_i I_i 2) \phi=\iint_A \vec{B} \cdot d\vec{A} 3) \phi_1=M_{12} I_2 The Attempt at...
18. ### Two solenoids and a ferrite bar

I have two solenoid coils, one is wounded on ferrite rod and other is wounded in larger diameter in proxmity of ferrite rod, see picture. It is used as wireless comm (simplex) between RX and TX where I use resonance on TX to maximise signal gains After bit of reading and now familar with mutual...
19. ### Mutual Inductance: Rectangle w/ Variable Height

Homework Statement I have a shape that is basically a rectangle but one side increase in height(shape length is L and it increases height at L/2). Which leaves me with two squares of different heights. Can I find the mutual inductance of each square and then add them up to find the inductance...
20. ### Trying to model mutual inductance with losses

So as a learning project I am trying to solve a transformer with losses but I am stuck. 1 coil L1 with N1 turns is excited by a sinusoidal voltage V1 with a resistor R1 in series. Wound around a common core with a second coil L2 with N2 turns and a resistor R2 also in series...
21. ### Why are there two terms of both mutal and self inductance

Homework Statement Given two inductors, connected in parallel connected to a battery, why do the following emf relations hold? $$\mathcal{E}_1 = - N_2 A \frac{d B}{d t} = -M\frac{d I_1}{d t } \\ \mathcal{E}_2 = -L_2 \frac{dI_2}{dt}- M \frac{dI_1}{dt}$$ See attachment ! Homework Equations...
22. ### How Do You Calculate Mutual Inductance in Toroidal Solenoids?

Homework Statement A toroidal solenoid with mean radius r and cross-sectional area A is wound uniformly with N1 turns. A second toroidal solenoid with N2 turns is wound uniformly on top of the first, so that the two solenoids have the same cross-sectional area and mean radius. What is the...
23. ### How to calculate the mutual inductance?

Homework Statement A long solenoid has a radius of 3 cm, 3000 turn per meter, and carries a current I = IOcos(ωt), where Io is 0.25 A and ω is 628 s−1 . It is placed through a circular loop of wire, radius 5 cm, which has resistance 100 Ω. The magnetic field in a solenoid is B = µonI. (a) Find...
24. ### Mutual inductance / equivalent inductor

Homework Statement Homework Equations See if you can show that L##_1## and L##_2## as in (a) can be replaced by the equivalent inductor L##_{eq}## as in (b): $$L_{eq} = \frac {L_1 L_2 - M^2 } {L_1 + L_2 - 2M }$$ The Attempt at a Solution Um, I don't really know where to start because I...
25. ### Flux Density in Mutual Induction Solenoid with Core

For a standard solenoid, I've found that B=μnI where μ = permeability of the core (4π×10^-7 for free space) n = number of coils I = current Firstly, is the permeability of soft iron 0.08, as I found? Primarily, however, I'm wanting to know if this still applies for a mutual induction apparatus...
26. ### Mutual inductance of a long wire and a triangular loop?

I originally posted this to the advanced homework -section, but maybe this isn't advanced enough to warrant being posted there :oops:. If a mod sees this, feel free to delete the original on the other forum. I'd do it myself, but I can't. 1. Homework Statement Calculate the mutual inductance for...
27. ### Current induced in concentric superconducting loops

Homework Statement Suppose you have two superconducting loops, concentric, in a plane. Also suppose that their radii, R2 (outer) and R1 (inner) have the same order of magnitude (so you can't assume B through the inner loop is constant everywhere over the inner loop's surface.) If a constant...
28. ### Help understanding Partial Mutual Inductance

I'm sure you are all familiar with calculating the inductance of a long transmission line. We first calculate the partial self inductance and we add to the partial mutual inductance due to the current in the other conductors. Looking at the image of a single-phase system, where I1 + I2 = 0...
29. ### Derivation of Mutual Inductance Energy

I've attached a picture of my book. So there is a figure of two inductors mutually connected. The book says that initially, current 1 and current 2 are zero. Then when current 1 goes from 0 to I1, the energy stored in circuit is only the energy in inductor 1. <-- This is my question, but...
30. ### Mutual Inductance Transfer function

Homework Statement Find Io(s)/Ii(s) Homework Equations Basic KVL laws. The Attempt at a Solution My idea is to start from the RHS of the circuit until I get a relation between Io(s) and Ii(s). Actually I stopped at this point, I wondered whether my approach is appropriate or not since...
31. ### Mutual Inductance Homework: What Happens?

Homework Statement We have coil connected to dc supply and a secondary coil connected to load. We cross the secondary coil with the primary and emf of mutual inductance is induced at that verry moment. Then the induction stops for there is no more change in the flux. However, if an emf is...
32. ### Parasitics in Solenoids: The Relationship Between AC Frequency and Induced EMF

If you have a one solenoid inside another (with the same number of coils of wire) the current is going through the inner one. How does the induced EMF in the outer one depend on the frequency of AC in the inner one
33. ### How to calculate mutual inductance of a rectangular loop

I am planning to build a rogowski coil but not the conventional one, which is a circular loop. Below is the example of a rogowski coil so you have the big picture of my question. In the picture, the current conducting wire (with current Ip) is encircled by a big circular loop rogowski coil...
34. ### Insights Misconceiving Mutual Inductance Coefficients - Comments

rude man submitted a new PF Insights post Misconceiving Mutual Inductance Coefficients Continue reading the Original PF Insights Post.
35. ### Calculating Self and Mutual Inductance: A Derivation of Formulas Using Solenoids

Homework Statement Homework Equations[/B] ∫BdL = μi Φ = BA (flux) S= NΦ/i (self inductance) M = NΦ/i (mutual inductance) The Attempt at a Solution a) ∫BdL = μi BL = μi B = μi/L since the solenoid has N1 turns B = μiN1/L b) flux Φ = BA = AμiN1/L self...
36. D

### Electromagnetic inductance -- Mutual inductance

I know that- The change in current of primary coil changes the magnetic flux linked with the secondary coil and this an emf will be induced in secondary coil (which also has an inductor in the circuit) so current grows in secondary coil and the current in secondary coil produces magnetic field...
37. ### Leq = (L1*L2-M^2)/(L1*L2-M^2)Hope this helps

Homework Statement FIGURE 4(a) shows two inductances connected in parallel across an a.c. supply. (a) Apply Kirchhoff’s voltage law to loop abef and to loop abcdef of the circuit. (b) Hence or otherwise obtain the current ratio I1/I2 in terms of the circuit inductances. (c) See if you can...
38. ### Mutual inductance interpretation

How to explain mutual inductance with the image I attached? There are two conducting frames, one has a source of DC and a variable resistor, the other just a galvanometer. What I should conclude from this picture that the flux is F1=alpha*I and F2=c*F1, and Ein=-M*dI/dt. How? Is the current I...
39. ### Mutual Inductance: Homework Solutions

Homework Statement Homework Equations The Attempt at a Solution
40. ### MATLAB Mutual inductance of two disk coils (MATLAB)

Hi, I'm been spending way too much time this weekend, wrestling with the equations provided in the paper [The mutual inductance of two thin coaxial disk coils in air, Babic S., DOI: 10.1109/TMAG.2004.824810], but I just can't seem to verify the results obtained in the examples in the journal...
41. ### What is the mutual inductance between a coil and an infinite straight line?

Homework Statement Find the mutual inductance between a coil with N loops and an infinite straight line with current I on its axis. Homework Equations M12 = M21 = flux 1/I 2 = flux 2/ I 1 emf = -d/dt flux i = emf /R R = eta*l/S The Attempt at a Solution I have done this...
42. ### Mutual Inductance (Parallel) Analysis Process

Homework Statement Please see attached images. 2. Relevant Questions I'm fairly certain the mesh equations are incorrect. I'm having a hard time accounting for the mutual inductance and the voltage/current loss between each mesh. When we account for the lost voltage (using j300 in...
43. ### Mutual Inductance Between a Coil and a Solenoid

Homework Statement A small, thin coil with N2 loops, each of area A2, is placed inside a long solenoid, near its center. The solenoid has N1 loops in its length L and has area A1. Find the mutual inductance as a function of θ, the angle between the plane of the small coil and the axis of the...
44. ### Mutual Inductance of RC Circuit on a Small Coil

Homework Statement My textbook has two problems, based on the same premises, but the solutions manual solves each of them differently, so I was wondering why? Here are the two problems... 1. In the circuit shown in Fig. P29.49, the capacitor has capacitance C = 20μF and is initially charged...
45. ### Mutual inductance in a circuit.

Homework Statement Derive TEC between terminals "ab". Homework Equations The Attempt at a Solution I figured I'd add the mutual inductances to the inductors, and solve it as a normal RLC circuit, since no current is passing through the 80j coil, it's inductance wouldn't change...
46. ### Find the mutual inductance between the coil and the wire in two ways

Homework Statement We have a toroidal coil, and an infinite wire that runs through it on its symmetry axis. (See picture) We need to find the mutual inductance between the coil and the wire in two ways: 1. By running a current through the wire, and finding the induced voltage in the...
47. ### Average power to ZL coupling coefficent and mutual inductance M?

Homework Statement In the circuit of Figure 4-2, let N1=2000 turns, N2=1000 turns, R=0, Z1=0 and ZL=300+j400 (Ω). If V1(max)=1500 V, what is the average power delivered to ZL? A. 5400 W B. 2700 W C. 337.5 W D. 675 WHomework Equations V2=(N2/N1)V1The Attempt at a Solution since turn factor is...
48. ### Understanding mutual inductance

In mutual inductance, energy transfer takes place from one circuit to another through magnetic flux. But while trying to understand the equations involved from the attached image, I am getting confused. If the current in the first coil gives rise to a flux \phi1 and only a part of it (\phi12)...
49. ### Mutual inductance between straight line cable & square shape Frame

Homework Statement Calculate mutual-inductance between straight line cable and square shape frame, as shown on picture. Homework Equations I am not sure which equation will be used here because as far as my knowledge goes , mutual inductance should be concerned with turns in...
50. ### Mutual Inductance Homework Solution

Homework Statement Derive an expression for the mutual inductance ,L12, for the case of the figure, assuming a current distribution: J_{2}(x)= F_{2}(x), h1<x<h2 or I_{2}(x)= ∫^{h_2}_{h_1} F_{2}(x)w_{2}dxHomework Equations L_{12}(x)=∅_{12}(x)/ i_{2}(x) The Attempt at a Solution In fact I don't...