How do inductors store energy as a magnetic field?

[Puglife]

My last lecture that I have had, was in inductors. My professor said that they resist changes in current, because they store energy inside the inductor as a magnetic field. I know that as soon as you shut off the energy between the inductor, it starts to dissipate, slowly, until it is completely depleted.

My question is this, how does an inductor actually store energy in it as a magnetic field, and why does the magnetic field instantly dissipate the second the current is shut off across it?

 

[my2cts]

This is an excellent question.
A good discussion can be found in Feynman's Lectures part 2, chapter 27. See the link below.
The discussion is about a capacitor storing energy in the E-field, but a similar story can be made for an inductor and the magnetic field.
Feynman clearly states this part of the theory with a certain amount of dissatisfaction. I quote:
"So our “crazy” theory says that the electrons are getting their energy to generate heat because of the energy flowing into the wire from the field outside. Intuition would seem to tell us that the electrons get their energy from being pushed along the wire, so the energy should be flowing down (or up) along the wire. But the theory says that the electrons are really being pushed by an electric field, which has come from some charges very far away, and that the electrons get their energy for generating heat from these fields. The energy somehow flows from the distant charges into a wide area of space and then inward to the wire."
"Finally, in order to really convince you that this theory is obviously nuts, ..."
http://www.feynmanlectures.caltech.edu/II_27.html

 

[anorlunda]

Magnetic? Yes.

Instantly? No.

You just said that it resists changes. That rules out instant changes in current.

The voltage across an inductor is $L\frac{dI}{dt}$. It can become very large when you try to stop I. That is how we generate sparks for the spark plugs in cars.

 

[Puglife]

Magnetic? Yes.

Instantly? No.

You just said that it resists changes. That rules out instant changes in current.

The voltage across an inductor is $L\frac{dI}{dt}$. It can become very large when you try to stop I. That is how we generate sparks for the spark plugs in cars.

I realize that it releases it gradually, sorry if I didn't make that clear, what I don't know is why and how it store energy and slowly releases it, instead of just instantly discharging

 

[Puglife]

This is an excellent question.
A good discussion can be found in Feynman's Lectures part 2, chapter 27. See the link below.
The discussion is about a capacitor storing energy in the E-field, but a similar story can be made for an inductor and the magnetic field.
Feynman clearly states this part of the theory with a certain amount of dissatisfaction. I quote:
"So our “crazy” theory says that the electrons are getting their energy to generate heat because of the energy flowing into the wire from the field outside. Intuition would seem to tell us that the electrons get their energy from being pushed along the wire, so the energy should be flowing down (or up) along the wire. But the theory says that the electrons are really being pushed by an electric field, which has come from some charges very far away, and that the electrons get their energy for generating heat from these fields. The energy somehow flows from the distant charges into a wide area of space and then inward to the wire."
"Finally, in order to really convince you that this theory is obviously nuts, ..."
http://www.feynmanlectures.caltech.edu/II_27.html

Ok, so how does that particularly apply to the question I asked, thank you for the nice response time.

 

[Puglife]

Magnetic? Yes.

Instantly? No.

You just said that it resists changes. That rules out instant changes in current.

The voltage across an inductor is $L\frac{dI}{dt}$. It can become very large when you try to stop I. That is how we generate sparks for the spark plugs in cars.

Also, if you shut off the current to a inductor, wouldn't the change in current be some arbitrary number over zero time? So wouldn't the voltage be infinite across its leads? Why does that not instantly disapate all energy in the inductor?

 

[my2cts]

Ok, so how does that particularly apply to the question I asked.

You asked "how does an inductor actually store energy in it as a magnetic field".
Feynman answers to the very similar question "how does a capacitor actually store energy in it as an electric field".

 

[anorlunda]

Also, if you shut off the current to a inductor, wouldn't the change in current be some arbitrary number over zero time? So wouldn't the voltage be infinite across its leads? Why does that not instantly disapate all energy in the inductor?

We don't get infinities in real life. When the voltage gets high, a spark jumps across the contacts of the switch and the current decreases in finite time.

A common error is to mix up ideal components with real life. The clue to that mix up, is when you get infinity for any answer. In real life, no R, L, C, V, I, or switch is purely ideal.

 

[tech99]

An inductor is analogous to a flywheel, having lots of inertia. It is hard to get the current flowing and hard to stop it. When you try to suddenly switch off, it is akin to applying a brake to a flywheel. It tries not to respond, but eventually the energy is dissipated as heat in whatever brake you use.

 

[Puglife]

An inductor is analogous to a flywheel, having lots of inertia. It is hard to get the current flowing and hard to stop it. When you try to suddenly switch off, it is akin to applying a brake to a flywheel. It tries not to respond, but eventually the energy is dissipated as heat in whatever brake you use.

I understand what it actually does, I just don't understand why? I don't see why the second you shut off the current across an inductor, how it is still able to maintain a magnetic field inside itself?

 

[tech99]

I understand what it actually does, I just don't understand why? I don't see why the second you shut off the current across an inductor, how it is still able to maintain a magnetic field inside itself?

If you think about a heavy flywheel spinning, it cannot maintain any momentum once you apply enough braking force to stop it. But it tries not to stop. Similarly, the inductor tries to stop you from switching off, by generating a high voltage across the switch gap. This is like the mechanical reaction against braking (F=-MA). But once you force the current down to zero, actually be applying a reverse voltage with the switch, the magnetic field has gone.

 

[Puglife]

If you think about a heavy flywheel spinning, it cannot maintain any momentum once you apply enough braking force to stop it. But it tries not to stop. Similarly, the inductor tries to stop you from switching off, by generating a high voltage across the switch gap. This is like the mechanical reaction against braking (F=-MA). But once you force the current down to zero, actually be applying a reverse voltage with the switch, the magnetic field has gone.

where does it get the energy to create that strong of a opposite voltage, if it is not connected to any source. My main issue is I don't see how it physically stores energy, rather, i see it as it allows energy to go through it, and that energy self inducts itself, and opposes itself, thus opposing current change. The issue with that way of thinking (which is probably totally wrong), is that the second the current stops flowing through it, the field should sease to exist, and thus the self induction instantly stops (i know this isn't what really happens now, but I don't know why at all). I would like to know the reasoning behind why it does what it does, instead of just know what it does. Thank you all very much for all of your help, you all are very kind to be helping me

 

[tech99]

where does it get the energy to create that strong of a opposite voltage, if it is not connected to any source. My main issue is I don't see how it physically stores energy, rather, i see it as it allows energy to go through it, and that energy self inducts itself, and opposes itself, thus opposing current change. The issue with that way of thinking (which is probably totally wrong), is that the second the current stops flowing through it, the field should sease to exist, and thus the self induction instantly stops (i know this isn't what really happens now, but I don't know why at all). I would like to know the reasoning behind why it does what it does, instead of just know what it does. Thank you all very much for all of your help, you all are very kind to be helping me

When a magnetic field is built, it is a store of energy. Maxwell originally used a mechanical analogy to develop his theories and it used spinning cells having inertia and momentum. The magnetic field will not collapse to nothing until you physically force the current down to zero. The inductor will not let you do this without a struggle.

 

[Puglife]

When a magnetic field is built, it is a store of energy. Maxwell originally used a mechanical analogy to develop his theories and it used spinning cells having inertia and momentum. The magnetic field will not collapse to nothing until you physically force the current down to zero. The inductor will not let you do this without a struggle.

why will it not let you force the current down to zero, and why is a electromagnetic field stored energy?

 

[meBigGuy]

Let's say you are passing 1 amp through an inductor with a parallel 1 ohm resistor and remove the supply.

The inductor has a magnetic field, and wants to maintain the 1 amp flow, so it will then create 1 volt to "send" the 1 amp through the 1 ohm resistor, reducing the magnetic field as it flows . The 1 amp reduces exponentially in time because a change in current is required to create the voltage across the resistor. This continues until the field is depleted.

If you do it with a 10 ohm resistor, it will initially generate 10 times the voltage to produce the initial 1 amp.

 

[NascentOxygen]

why will it not let you force the current down to zero, and why is a electromagnetic field stored energy?

It will, but you have to cause its current to reach zero before all its energy has been drained.

A magnetic field around a solenoid represents stored energy, because you can use it to power an electric or electronic circuit after all other voltage sources have been removed.

 

[my2cts]

why will it not let you force the current down to zero, and why is a electromagnetic field stored energy?

You are now ready to read the Feynman Lecture and see that even he did not understand it !

 

[Puglife]

It will, but you have to cause its current to reach zero before all its energy has been drained.

A magnetic field around a solenoid represents stored energy, because you can use it to power an electric or electronic circuit after all other voltage sources have been removed.

How does the magnetic field not instantly shut off as soon as you pull the switch? Like how does it physically store the energu

 

[Puglife]

You are now ready to read the Feynman Lecture and see that even he did not understand it !

If he does not know the answer, does anyone? Is their an actual concrete answer? And if he didn't know it, then what is the lecture on? And how will it help me?

 

[Puglife]

When a magnetic field is built, it is a store of energy. Maxwell originally used a mechanical analogy to develop his theories and it used spinning cells having inertia and momentum. The magnetic field will not collapse to nothing until you physically force the current down to zero. The inductor will not let you do this without a struggle.

So does it have yl do with maxwell theories on electromagnetic waves? Does it propionate because it turned into a em wave?

 

[NascentOxygen]

How does the magnetic field not instantly shut off as soon as you pull the switch? Like how does it physically store the energu

As others have pointed out, it is not possible to instantly halt current in an inductor. If you try to, by flipping open a switch, a high voltage is created and this jumps across the switch contacts, ionizing the air and heating the air and switch and delivering the inductor's stored energy as the equivalent in heat. The faster you try to operate the switch, the greater the voltage spark produced so it is still able to jump across the wider air gap. Some of the energy radiates away as radio waves, you hear this as static on your AM radio when there's an electrical spark nearby.

inductor voltage = L.$\frac {di} {dt}$

 

[Puglife]

As others have pointed out, it is not possible to instantly halt current in an inductor. If you try to, by flipping open a switch, a high voltage is created and this jumps across the switch contacts, ionizing the air and heating the air and switch and delivering the inductor's stored energy as the equivalent in heat. The faster you try to operate the switch, the greater the voltage spark produced so it is still able to jump across the wider air gap. Some of the energy radiates away as radio waves, you hear this as static on your AM radio when there's an electrical spark nearby.

inductor voltage = L.$\frac {di} {dt}$

I understand what it physically does, and exactly what happened in the real world, I just don't know why it does that. I know that it resists current change, what i don't know is why, is it that it produces a electromagnetic induction in the opposite direction of current flow, thus producing an opposing voltage? I also know that after the current stops completely, it will turn into a supply of voltage to maintain its previous current, I just don't know the reasoning behind why it does that (other than it resists changes to current, which isn't the answer I am looking for). I also do not know how it is possible for it to "store" energy as a magnetic field, the magnetic.
Thank you all for your help though, I appreciate you all spending the time to help me.

 

[NascentOxygen]

I also know that after the current stops completely, it will turn into a supply of voltage to maintain its previous current, ✘

You haven't got it right. Current doesn't reach zero until all stored energy has been delivered.

 

[Puglife]

You haven't got it right. Current doesn't reach zero until all stored energy has been delivered.

I see where the confusion in what I was trying to say came from, and it is this, when you shut off the current you are supplying to the inductor, it physically supplys its own voltage to maintain its own current, until the energy stored goes away (that was totally my bad, I worded it in a ridiculous manner), but that didnt answer any of my other questions, not help me in any way.

Also thank you for your good response time, its really appreciated!

 

[marcusl]

My main issue is I don't see how it physically stores energy

Energy storage in an electric field works like this. It takes energy to move and hold charges in place to create an electric field. The work done in assembling the configuration and building the field is not lost--it is said to be stored in the field, and can be recovered (again as work) by allowing the charges to move away back to their original locations. The energy was thus "stored" in the field.

To generate a current-based magnetic field, work must be done to hold charges together and to cause them to move in a coordinated way that we call a current. That work is, likewise, stored in the field and may be recovered if the current is allowed to decay. The recovered energy can be expended as work done on resistances in a circuit that is connected to the field/current assembly (assuming that it involves wires). The work is driven by a potential (a.k.a. EMF or voltage) that appears as the current decays. A voltage or potential, in fact, has units of energy (indeed, high energy particle physicists measure energy with the unit "electron volts"), so everything is consistent.

 

[tech99]

Energy storage in an electric field works like this. It takes energy to move and hold charges in place to create an electric field. The work done in assembling the configuration and building the field is not lost--it is said to be stored in the field, and can be recovered (again as work) by allowing the charges to move away back to their original locations. The energy was thus "stored" in the field.

To generate a current-based magnetic field, work must be done to hold charges together and to cause them to move in a coordinated way that we call a current. That work is, likewise, stored in the field and may be recovered if the current is allowed to decay. The recovered energy can be expended as work done on resistances in a circuit that is connected to the field/current assembly (assuming that it involves wires). The work is driven by a potential (a.k.a. EMF or voltage) that appears as the current decays. A voltage or potential, in fact, has units of energy (indeed, high energy particle physicists measure energy with the unit "electron volts"), so everything is consistent.

I don't think "allowed to decay" is quite accurate. To stop the current, we have to apply a force, a reverse voltage, just like stopping a flywheel, and the energy stored in the inertia of the system does work against our force by producing movement or current.

 

[Puglife]

Energy storage in an electric field works like this. It takes energy to move and hold charges in place to create an electric field. The work done in assembling the configuration and building the field is not lost--it is said to be stored in the field, and can be recovered (again as work) by allowing the charges to move away back to their original locations. The energy was thus "stored" in the field.

To generate a current-based magnetic field, work must be done to hold charges together and to cause them to move in a coordinated way that we call a current. That work is, likewise, stored in the field and may be recovered if the current is allowed to decay. The recovered energy can be expended as work done on resistances in a circuit that is connected to the field/current assembly (assuming that it involves wires). The work is driven by a potential (a.k.a. EMF or voltage) that appears as the current decays. A voltage or potential, in fact, has units of energy (indeed, high energy particle physicists measure energy with the unit "electron volts"), so everything is consistent.

Doesn't the heat dissipation, as well as the current into a resistor equaling the current out of a resistor, or in this case wire, conserve it's energy? How does the production if an electromagnetic field, continuously follow the conservation of energy. What is the energy loss in the circuit, that physically causes the electromagnetic field to form? where does the energy to do the initial work to create the field come from, because isn't the entirety of the energy drop from resistance dissipated through heat?

 

[anorlunda]

Doesn't the heat dissipation, as well as the current into a resistor equaling the current out of a resistor, or in this case wire, conserve it's energy? How does the production if an electromagnetic field, continuously follow the conservation of energy. What is the energy loss in the circuit, that physically causes the electromagnetic field to form? where does the energy to do the initial work to create the field come from, because isn't the entirety of the energy drop from resistance dissipated through heat?

There are such things as superconducting electromagnets with zero resistance, they store energy too. So it is better to divorce resistance from inductance in your thinking.

 

[Puglife]

There are such things as superconducting electromagnets with zero resistance, they store energy too. So it is better to divorce resistance from inductance in your thinking.

ok, in that case, where does the energy physically come from, in order to produce the magnetic field, if their is no energy loss in terms of electricity in the circuit? does it not apply to conservation of energy for some reason?

 

[anorlunda]

The energy comes from the external circuit that is forcing the current and supplying the voltage. P=V*I.

 

[Puglife]

The energy comes from the external circuit that is forcing the current and supplying the voltage. P=V*I.

yes, but let's say you have a super conductor that produces a magnetic charge, then the voltage into the circuit is the same as the voltage out of it (kvl for a standard loop) and also the current into a zero resistance node is also the same as the current going out of it, their is no loss of energy in that circuit what so ever, so where does the energy come from, it has to be conserved some how., and if their is no electrical loss of energy, at all, but their is also an electromagnetic field produced with the zero loss, then their is more energy being released by the system then their is coming into it, is it not?

 

[anorlunda]

yes, but let's say you have a super conductor that produces a magnetic charge, then the voltage into the circuit is the same as the voltage out of it (kvl for a standard loop) and also the current into a zero resistance node is also the same as the current going out of it, their is no loss of energy in that circuit what so ever, so where does the energy come from, it has to be conserved some how., and if their is no electrical loss of energy, at all, but their is also an electromagnetic field produced with the zero loss, then their is more energy being released by the system then their is coming into it, is it not?

The answer is in #30. Your concepts of energy in circuits are very wrong. Search for a tutorial on basic electric circuits, and study them until you understand the answer.

 

[Puglife]

The answer is in #30. Your concepts of energy in circuits are very wrong. Search for a tutorial on basic electric circuits, and study them until you understand the answer.

What do you mean #30 and how is it wrong, if you have a super conductor that has zero resistance and no energy loss in the circuit, then how can their be a production of an electromagnetic field?

 

[anorlunda]

It means post number 30 in this thread.

 

[Puglife]

It means post number 30 in this thread.

Oh, so all of the power (watts) in a circuit goes into heat light and em field production? So with the superconductor example, 100% of all the power cones from the wattage in the circuit?

 

[marcusl]

I don't think "allowed to decay" is quite accurate. To stop the current, we have to apply a force, a reverse voltage, just like stopping a flywheel, and the energy stored in the inertia of the system does work against our force by producing movement or current.

Not necessarily. We can use a switch to connect the inductor to a resistance and let the current decay exponentially as field energy dissipates in the resistance.

 

[marcusl]

Doesn't the heat dissipation, as well as the current into a resistor equaling the current out of a resistor, or in this case wire, conserve it's energy? How does the production if an electromagnetic field, continuously follow the conservation of energy. What is the energy loss in the circuit, that physically causes the electromagnetic field to form? where does the energy to do the initial work to create the field come from, because isn't the entirety of the energy drop from resistance dissipated through heat?

Sorry, no part of this post makes sense to me. I described the process by which the creation of a field requires work to be done from an external source, and the sense in which that work is stored as energy in the field. Please rephrase if you still have questions.

 

[NascentOxygen]

ok, in that case, where does the energy physically come from, in order to produce the magnetic field, if their is no energy loss in terms of electricity in the circuit? does it not apply to conservation of energy for some reason?

It can be summarised like this:
to build the field requires energy, so we apply a voltage and the inductor draws an ever increasing current,
to maintain the field requires a fixed current but [ideally] no voltage,
to collapse the field requires that energy be taken from the inductor, it can be reabsorbed by the source or electronically switched into another circuit.

Where there is no resistance there are no i².R losses, and the energy returned when the field decays equals the energy that was earlier supplied in building it.

 

[marcusl]

Precisely.

 

[Puglife]

It can be summarised like this:
to build the field requires energy, so we apply a voltage and the inductor draws an ever increasing current,
to maintain the field requires a fixed current but [ideally] no voltage,
to collapse the field requires that energy be taken from the inductor, it can be reabsorbed by the source or electronically switched into another circuit.

Where there is no resistance there are no i².R losses, and the energy returned when the field decays equals the energy that was earlier supplied in building it.

So the energy that started to build the field was the power of the circuit? So in the case of the super conductor, the power of the magnetic field would be the full vi because the power I'd not being dissipated in any other way?

Also, thank you all for being patient with me, I am really trying to completely understand this

 

[marcusl]

Power and energy are different: power is a change in energy per unit time.

 

[Puglife]

Power and energy are different: power is a change in energy per unit time.

ok, but none the less, does the energy from the em field come from the power? (energy over time)

 

[marcusl]

The energy put into the EM field is supplied by the external circuit (integral of power over time, if you want to think in terms of power).

 

[NascentOxygen]

So the energy that started to build the field was the power of the circuit?

It came from the circuit's input power.

So in the case of the super conductor, the power of the magnetic field would be the full vi because the power I'd not being dissipated in any other way?

Because v and i are not both constant, it's not very informative to speak of their product, vi or power, that's why I explained the cycle in terms of energy. Conservation of energy when none is lost as heat, means that averaged over time
Electrical Energy in = Electrical Energy out

 

[Puglife]

It came from the circuit's input power.

Because v and i are not both constant, it's not very informative to speak of their product, vi or power, that's why I explained the cycle in terms of energy. Conservation of energy when none is lost as heat, means that averaged over time
Electrical Energy in = Electrical Energy out

ok, so as per my original question, i know that the energy form the magnetic field stays their, but how does it stay their without a constant energy being input into it?

 

[NascentOxygen]

ok, so as per my original question, i know that the energy form the magnetic field stays their, but how does it stay their without a constant energy being input into it?

The current is being held fixed and this maintains the field. No work is needed for this as the ideal inductor is lossless.

Just as no work is involved in keeping a rubber band stretched---you just stretch it over two fixed pegs spaced well apart on the wall.

(If using a lossless inductor you can just connect the two ends of the winding together and let the current go round and round forever.)

 

[davenn]

but how does it stay their without a constant energy being input into it?

Here's a pretty respectable description...

This does come up time to time and it isn't a matter of semantics. Back EMF simply is not the spike that you get from a coil when the field collapses.

You charge a coil - lenz's law describes the counter current or back emf that opposes the forward current and resists the forward current's ability to bring the coil's charge up...

Once the coil is charged and you disconnect power, the spike you get back is the "inductive spike" or "transient spike."

You can see Lenz's law here:
http://www.energeticforum.com/redirect-to/?redirect=http%3A%2F%2Fwww.mwit.ac.th%2F%7EPhysicslab%2Fhbase%2Felectric%2Ffarlaw.html%23c2
It is at the bottom.

Look at this nice simple answer:
WikiAnswers - What is the formula for transient spike computation in an inductive load

"E=I x R. The inductive spike occurs as the circuit is opened. The collapsing magnetic field causes the inductor to become the source of the circuit. For example consider a circuit consisting of a 10 volt battery, a 10 mh inductor, and a 10 ohm resistor all in series. With the switch closed, 1 amp will flow through the circuit (after 5 mS). The 5 mS is the time it takes the current to rise from 0 to 1 amp. This is given by the formual TC=L/R where TC is the time constant in seconds, L is the inductance in henries, and R is the resistance in ohms. It takes 5 time constants for the current to reach the maximum current which is determined by I=E/R (Ohm's Law). The delay is caused by the counter EMF generated in the coil as flux lines cut through adjacent turns of the inductor. After 5 time constants, the current is at 1 amp. When we open the switch, it will take 5 time constants for the current to drop to 0 amps. However, this will not be 5 mS because the resistance is now much larger do to the opening switch contacts. The voltage across the switch contacts will be whatever is necessary to maintain the current flow for the 5 time constants. After one time constant, the current will have dropped to 32% of the maximum current or in this case, 0.32 amps. If the resistance of the switch gap is 1 megohm, the the voltage will be 320,000 volts. More than enough to ionize the air and create a conductive path. If we assume an average resistance of 1 megohm, it will take 50 nS for the current to drop to 0. Of course during this time, the switch contact gets zapped. Placing a diode across the inductor such that the diode is reverse biased with the switch closed will give the current an alternate path as the polarity of the inductor reverses when the magnetic field collapses and the inductor becomes the source. This lowers the voltage from 1,000,000 volts to 0.7 volts. The downside is that the time it takes for the current decrease increases bo the ratio of 1,000,000/0.7. In a relay, this may cause the relay to "chatter" when opening. Adding a zener diode in series anode to anode with the spike suppressing diode will alleivate most chattering problems. A 34.3 volt zener will raise the voltage from 0,7v to 35v and shorten the time by a factor of 50 (35/.0.7). "

Dave

 

[NascentOxygen]

it doesn't ! ... as soon as the external power source is removed the magnetic field starts to collapse

As it collapses it cuts through the windings of the inductor. This generates a voltage (EMF) across the inductor
with a current flowing in the opposite direction to the original externally supplied current

Dave

This is not correct.

 

[Puglife]

The current is being held fixed and this maintains the field. No work is needed for this as the ideal inductor is lossless.

Just as no work is involved in keeping a rubber band stretched---you just stretch it over two fixed pegs spaced well apart on the wall.

(If using a lossless inductor you can just connect the two ends of the winding together and let the current go round and round forever.)

oh, ok, that makes total sense in that case, so if i have any coil of wire, it will somewhat resist changes in current, just because it takes work to decrease the current in it, which is supplied by the resistance?

 

[Puglife]

oh wow thanks man, i completely understand it now, i watch some videos on lenz law , and I am perfect now, that was the most helpful answer i have ever gotten on physics forums, thank you so so much!