# Mutual inductance

## 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 induced in the 2coil there will be current witch will create magnetic field wich will cross the primary coil and by Lenz law will induce in it emf that will create another magnetic field that will continue this circle for ever. But thats not what happens. So my question is what heppens?

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## The Attempt at a Solution

gneill
Mentor
Lenz' Law is the electrical equivalent of Newton's Third Law for mechanics. The EMF that is induced opposes the agency that is inducing it. Using a mechanical analogy, where a force is applied to an object, the Third Law force that the agency applying the force "feels" is a result of the inertia of the second object. Note that we don't expect a never ending feedback loop of increasing forces to occur between the agency and object.

There's no time delay implied with Lenz' Law. All currents and reactional currents or emfs occur concurrently. So you don't get to induce a current in the secondary separately from the emf that is induced in the primary opposing the change, just as you don't expect a delay between applying a force to an object and the Newton's Law opposing force.

If you want to investigate this in detail the best way to do so would be to write and solve the differential equations governing such a circuit. You'll see that there are time dependent effects due to real-world characteristics of any components (largely unavoidable wire resistance) that manifest as "decay" shaping of current or voltage waveforms.

If you happen to like analogies, then the mechanical analogy for a transformer is the lever. All the mechanical characteristics that a lever demonstrates with forces and motions and masses have their counterparts in the electric version, including the effects of inertia being coupled on either side of the lever.

Thank you! The analogy with Newtons third law was great. So we expect those two opposite magnetic fields to ballance eachother?

gneill
Mentor
Thank you! The analogy with Newtons third law was great. So we expect those two opposite magnetic fields to ballance eachother?
I'm not sure what you mean by balance here, but the magnetic flux involved in mutual inductance comprises lines of flux that pass through both coils. Any effect that such a line of flux has on one coil it must have on the other (proportionally with the number of turns in the coil, of course). There can be no lines of flux that pass through both coils ("mutual") which do not affect both coils reciprocally.

To return to the lever analogy, forces applied at either end of the lever are transmitted to the other end via the lever arm, and any motion of the lever ends is constrained by the lever coupling; lever ends cannot move independently, being joined and constrained by the stiff lever arm. Force multiplied by velocity at one end equals force multiplied by velocity at the other end. That is, the power at each arm of the lever balances. In an ideal transformer, the same holds for voltage and current at each coil: ##V_p I_p = V_s I_s##.

• Grim Arrow
I'm not sure what you mean by balance here, but the magnetic flux involved in mutual inductance comprises lines of flux that pass through both coils. Any effect that such a line of flux has on one coil it must have on the other (proportionally with the number of turns in the coil, of course). There can be no lines of flux that pass through both coils ("mutual") which do not affect both coils reciprocally.

To return to the lever analogy, forces applied at either end of the lever are transmitted to the other end via the lever arm, and any motion of the lever ends is constrained by the lever coupling; lever ends cannot move independently, being joined and constrained by the stiff lever arm. Force multiplied by velocity at one end equals force multiplied by velocity at the other end. That is, the power at each arm of the lever balances. In an ideal transformer, the same holds for voltage and current at each coil: ##V_p I_p = V_s I_s##.

[QUOTE="gneill, post: 5279366

''If you want to investigate this in detail the best way to do so would be to write and solve the differential equations governing such a circuit'' Hello, that confuses me as well. You were talking about some equations, can you give them to me or atleast some link?

gneill
Mentor
[QUOTE="gneill, post: 5279366

''If you want to investigate this in detail the best way to do so would be to write and solve the differential equations governing such a circuit'' Hello, that confuses me as well. You were talking about some equations, can you give them to me or atleast some link?
Examples can be found online by searching for terms like "mutual inductance circuit example" or "mutual inductance transient response", although a course textbook would be a safe bet. I'm partial to "An Introduction to Electrical Circuit Theory" by G Williams. It covers inductance and mutual inductance very well in both differential equation and phasors.

Examples can be found online by searching for terms like "mutual inductance circuit example" or "mutual inductance transient response", although a course textbook would be a safe bet. I'm partial to "An Introduction to Electrical Circuit Theory" by G Williams. It covers inductance and mutual inductance very well in both differential equation and phasors.
Thank you!

[QUOTE="gneill, post: 5279366

''If you want to investigate this in detail the best way to do so would be to write and solve the differential equations governing such a circuit'' Hello, that confuses me as well. You were talking about some equations, can you give them to me or atleast some link?
Try to imagine that like this:Since two magnetic fields with the same polarity cant exist in the same place at the same time, they try to repel eachother. However the coils that created them cant move. Becouse of that the fields now began to conquer each other and each coil try to decrease the magnetic field strenght of the other. However if the secondary coil block all the flux from the primary, there will be no emf in it and after a short duration its magnetic field will dissapear and the primary coil will again induce in it emf. So the effect is that the secondary coil always follow or is behind the primary. Is that right Gneill? sry for that last question from me to you, but it is my blessing and curse that i cant study something without fully understanfing it:-D

gneill
Mentor
Lines of flux loop through both coils, so the proposed concept that one coil could "block" the flux from another doesn't work. Also, designating one coil as a primary and the other as secondary is practical jargon for transformers and doesn't really have a basis in the physics of the situation other than it's handy for electrical engineers to label them that way to suggest an "input" and and "output" for signal or power flow. One could place sources on either or both sides of a transformer and apply the same equations and analysis methods.

It is tempting to think of the stimulation and induced currents and interactions as being sequential events, one triggering the other followed by the induced current in turn inducing a current into the other coil and so on, with some tiny delay between the events. But in reality it all happens simultaneously. Just like the lever arm remains rigid and motions are synchronized at either end.

• Grim Arrow
Lines of flux loop through both coils, so the proposed concept that one coil could "block" the flux from another doesn't work. Also, designating one coil as a primary and the other as secondary is practical jargon for transformers and doesn't really have a basis in the physics of the situation other than it's handy for electrical engineers to label them that way to suggest an "input" and and "output" for signal or power flow. One could place sources on either or both sides of a transformer and apply the same equations and analysis methods.

It is tempting to think of the stimulation and induced currents and interactions as being sequential events, one triggering the other followed by the induced current in turn inducing a current into the other coil and so on, with some tiny delay between the events. But in reality it all happens simultaneously. Just like the lever arm remains rigid and motions are synchronized at either end.
Ok, thanks!