Energy transfer in electromagnetic induction

In summary: Since the field lines extend outward from the magnet, the speed at which the field lines can propagate is limited by the speed of light. Thus, there will be a delay before the field lines reach the coil.
  • #36
I know I haven't immediately answered your questions, but I have not thought about this problem before, so I am trying to start with the principles that I am most certain should apply to this situation.

So, for the questions. Are they real waves? Um, I guess they satisfy the inhomogeneous wave equations. So yes? But then by this definition, every classical electromagnetic phenomena involves real waves. If we instead define a real wave as being oscillatory, then I guess generally the waves in this case would be partly real and partly not.

I would expect the accelerating magnet to emit EM energy even if the coil was not there. For example, if the magnet was made of a coil with current flowing through it, then when we nudge the magnet, we are accelerating charges, which generally gives off EM radiation.
 
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  • #37
entropy15 said:
Are these waves real, like normal electromagnetic waves?
If the moving magnet is emitting an electromagnetic wave, it should do so only if the coil is present. Because if there was no coil there would be
nothing to absorb this wave. Also if there is no coil the magnet will not experience resistance meaning that it has not emitted the wave.
But how can the magnet know instantantaneously (as soon as it starts moving) that there is a coil at a distance x?

I would guess that EM waves would be created by the acceleration, but I really don't know. I know accelerating a single charge will do this, but I don't know about a magnet. IF it emits EM waves then it must feel a small amount of "resistance" from the emission. This would be separate resistance from the resistance felt due to induction in the coil, and would only happen during the acceleration. Once it was moving steadily it would not emit EM radiation since it isn't accelerating. (That of course is IF it emits EM radiation in the first place)
 
  • #38
Drakkith said:
IF it emits EM waves then it must feel a small amount of "resistance" from the emission. This would be separate resistance from the resistance felt due to induction in the coil, and would only happen during the acceleration. Once it was moving steadily it would not emit EM radiation since it isn't accelerating. (That of course is IF it emits EM radiation in the first place)

The energy transfer here should be taking place due to the induction and not through radiation (which even if present should be small and can be neglected as well).

The delay for the magnet to experience resistance due to the current in the coil seems to be
2x/c.

Indeed, If we follow the classical approach the delay seems to be 2x/c. But if we look at it from QED perspective it seems to be 0. (Wheeler Feynman absorber theory)

Can we throw more light on it looking at it from the relativity perspective?
After all magnetic field can be explained as an effect due to the "length contraction" involving moving charges using theory of relativity.

I have seen papers which explain the origin of magnetic fields using relativity. Most of them have to do with the forces of attraction/repulsion between two wires carrying current.
But I have not come across any which explain electromagnetic induction with the same approach.

I know it would be too complicated, but in case any of you have come across it, please help.
 
  • #39
Drakkith has got a good point. There are two different situations 1) considering a magnet which is being given a 'nudge' by some person. 2) considering a magnet which is moving toward the coil, with no 'outsider' forces.

I have mostly been talking about what happens when the magnet is given a 'nudge' i.e. acceleration. In this case, there is a delay before the effect is felt by the coil. I am pretty sure that Wheeler Feynman absorber theory also predicts that there is a time delay. But because I don't know much QFT, I can't say with complete certainty.

Now in the case when the magnet is moving freely (not being 'nudged'), then I am not so sure about whether there is a delay in the reaction force being felt, because in this case, at any particular time, there is already a magnetic field traveling between the magnet and the coil (which is due to the magnet moving at an earlier time).
 
  • #40
Are these waves real, like normal electromagnetic waves?
If the moving magnet is emitting an electromagnetic wave, it should do so only if the coil is present. Because if there was no coil there would be
nothing to absorb this wave. Also if there is no coil the magnet will not experience resistance meaning that it has not emitted the wave.
But how can the magnet know instantantaneously (as soon as it starts moving) that there is a coil at a distance x?

It is just normal electromagnetic wave. When the magnet is nudged, the surface currents on it get nudged too and electromagnetic waves start to propagate out of the surface. In standard theory with retarded fields, there is no immediate effect of the coil on the magnet; this comes only later, after time 2x/c.

However, the magnet will feel small resistance immediately. This is due to the fact that one part of the surface current will act on another, an in case the magnet is accelerated, these forces do not cancel each other but tend to act against the acceleration. This is sort of a "self-inductance" effect.

Later, after time 2x/c, the wave from the coil will come and damp the magnet as well. This will be typically much greater effect (sort of "mutual inductance").
 
  • #41
Jano L. said:
However, the magnet will feel small resistance immediately. This is due to the fact that one part of the surface current will act on another, an in case the magnet is accelerated, these forces do not cancel each other but tend to act against the acceleration. This is sort of a "self-inductance" effect.

Later, after time 2x/c, the wave from the coil will come and damp the magnet as well. This will be typically much greater effect (sort of "mutual inductance").

Since the self inductance effect is very small let's consider only the mutual inductance.

Suppose that the magnet is initially at rest.
It is given a push at time t=t1. Let's assume that the kinetic energy transferred to the magnet due to this push is Ek.
This kinetic energy may decrease immediately due to radiation or self inductance but the effect is negligible.

Now at time t=t1+(x/c) we have the current induced in the coil and it has gained energy due to this induced current.

Now since the magnet does not experience any resistance till t1+(2x/c) i.e any considerable resistance we can see that the magnet does not lose the kinetic energy acquired by it during the initial push till t1+(2x/c).

So between t1+(x/c) and t1+(2x/c) we have this energy in the coil as well as in the kinetic energy of the magnet.

The kinetic energy of the magnet is the cause for the current to be induced in the coil.
The magnet just transfers its kinetic energy to the coil through mutual induction.
So should not the kinetic energy of the magnet decrease before the current is induced in the coil?
 
  • #42
The kinetic energy of the magnet is the cause for the current to be induced in the coil.

Not exactly. It is better to say that the electromagnetic forces due to the magnet drive the currents in the coil.

The magnet just transfers its kinetic energy to the coil through mutual induction.

This is also not accurate enough. If we want to use the energy concept, we can, but we have to keep in mind all contributions to the energy. In this case, besides the magnet and the coil, there is also energy distributed throughout the remaining space. It is better to say that when the wave hits the coil, the field in the vicinity of the coil and inside it supply the energy for the animation of the currents.

So should not the kinetic energy of the magnet decrease before the current is induced in the coil?

It should not. Again, try to think of this in terms of the force - the response from the coil has not arrived yet, so there is no force acting on the magnet in the time interval x/c,2x/c.

You are probably worried about conservation of energy, but I think there is no problem. The currents in the coil get their energy from the field near the wires. Eventually, the magnet will lose some kinetic energy, but this is merely an after-effect.
 
  • #43
Jano L. said:
You are probably worried about conservation of energy, but I think there is no problem. The currents in the coil get their energy from the field near the wires. Eventually, the magnet will lose some kinetic energy, but this is merely an after-effect.

The current strength is proportional to the velocity of the magnet. The faster the magnet moves, more is the current.
The energy stored inside the magnetic field is constant. If the current gets energy from the field surrounding the coil, how can it obtain more and more energy from this field as the velocity of the magnet increases.

If the magnet is moving with a sufficiently high velocity the current induced in the coil may increase beyond what the surrounding magnetic field can provide.
 
  • #44
Jano L. said:
It should not. Again, try to think of this in terms of the force - the response from the coil has not arrived yet, so there is no force acting on the magnet in the time interval x/c,2x/c.
If we consider the Wheeler Feynman absorber theory the response from the coil arrives as advanced waves from the future to the instant when the magnet starts to move.
So this should get rid of the energy conservation problems.

In this case the resistance is felt immediately rather than 2x/c.
 
  • #45
If the current gets energy from the field surrounding the coil, how can it obtain more and more energy from this field as the velocity of the magnet increases.

The energy of the field is not just magnetic; it has electric component as well. This has to be so, for pure magnetic field could not induce currents in the coil.

The energy of the field is the higher the higher is the velocity of the magnet. We can be sure that there is always enough energy present to maintain the energy conservation, because we have the Poynting theorem; this shows that the energy is conserved locally, and moves through space like fluid..

I agree it is difficult to imagine this in such complicated process, but there is an alternative way of description, via EM forces, which makes this much more clear. According to the Faraday law, the magnitude of the electric field due to magnet animating the currents is the higher the higher is the velocity of the magnet; the higher the electric field, the stronger currents get induced.
 
  • #46
entropy15 said:
The current strength is proportional to the velocity of the magnet. The faster the magnet moves, more is the current.
The energy stored inside the magnetic field is constant. If the current gets energy from the field surrounding the coil, how can it obtain more and more energy from this field as the velocity of the magnet increases.
When you have a moving magnetic field then you also induce an E field according to Faraday's law. This E field also contains energy. As you push the magnet faster your dB/dt is greater and therefore the induced E field is also greater. The extra energy you are worried about is in this induced E field.

I see the scenario as follows:
1) magnet and coil at rest wrt each other, no forces
2) force on magent to accelerate magnet (extra force required in order to generate E field)
3) EM wave propagates at c to coil
4) changing current induced in coil
5) changing field produced by coil
6) EM wave propagates at c to magnet
7) coil field opposes motion of magnet

I recommend against throwing unnecessary quantum concepts into any discussion which can be done purely classically. Generally it adds more confusion than understanding.
 
  • #47
entropy15 said:
Now since the magnet does not experience any resistance till t1+(2x/c) i.e any considerable resistance we can see that the magnet does not lose the kinetic energy acquired by it during the initial push till t1+(2x/c).
No, the point is that when we give the magnet a 'nudge', we are putting energy into the electromagnetic field. So there is an immediate resistance, but not due to mutual inductance. (We will feel a resistance even if there is no coil). And if there is a coil, then we also get a delayed resistance due to mutual inductance.

Edit: So I guess I'm saying that if we only considered mutual inductance, then energy is not conserved when we give the magnet a nudge. (But this is because we are not considering the whole picture).
 
  • #48
entropy15 said:
If the magnet is moving with a sufficiently high velocity the current induced in the coil may increase beyond what the surrounding magnetic field can provide.
I don't understand what you mean here.
 
  • #49
BruceW said:
No, the point is that when we give the magnet a 'nudge', we are putting energy into the electromagnetic field. So there is an immediate resistance, but not due to mutual inductance. (We will feel a resistance even if there is no coil). And if there is a coil, then we also get a delayed resistance due to mutual inductance.

Hi Bruce,
Thanks for replying to my queries.

One more thing here, suppose that we replace the magnet with an electromagnet. The current in the electromagnet is controlled by a switch. Also we will remove the coil.(which was originally placed at a distance x)

Initially the electromagnet is not powered on and hence no magnetic field would be present.
Now we nudge this electromagnet so that it starts moving at a constant velocity.

Next the electromagnet is switched on so that it produces a magnetic field. Now since it is moving, it should try putting energy to the electromagnetic field.

So won't this oppose the current flowing in the electromagnet itself? trying to decrease the magnetic field.
 
  • #50
BruceW said:
I don't understand what you mean here.

I was assuming that the energy in the electric field was constant, but as DaleSpam has pointed out the faster the magnet moves more the energy in the electric field, so this should not be a problem.
 
  • #51
entropy15 said:
Next the electromagnet is switched on so that it produces a magnetic field. Now since it is moving, it should try putting energy to the electromagnetic field.

So won't this oppose the current flowing in the electromagnet itself? trying to decrease the magnetic field.

No, from the frame of the electromagnet it is stationary and it has no field built up prior. When you had the regular magnet, you also had a magnetic field built up which has its own frame of reference. When the magnet was bumped the two frames were no longer stationary with each other and the movement caused the field to oppose the acceleration and movement for a moment.
 
  • #52
Drakkith said:
No, from the frame of the electromagnet it is stationary and it has no field built up prior. When you had the regular magnet, you also had a magnetic field built up which has its own frame of reference. When the magnet was bumped the two frames were no longer stationary with each other and the movement caused the field to oppose the acceleration and movement for a moment.

Yes, I can see that now. Thanks much.

But what if we repeat the original experiment of the magnet and coil by replacing the permanent magnet with this electromagnet.

Initially the electromagnet is turned off. Then it is nudged so that it moves at a constant velocity v.
Now we power on the electromagnet at instant t=t1.
When will the current be induced in the coil (which is at a distance x) and when will the electromagnet experience resistance?

Would the results be similar to what we get when we had the permanent magnet there or is it different with an electromagnet?
 
  • #53
What do you think? What would you expect to be similar and what would you expect to be different in this case?
 
  • #54
I am impressed by entropy15's perseverance at trying to understand this problem fully :) The point I think he is trying to make is that when the electromagnet gets switched on, there is a delay of 2x/c before it feels the resistance due to mutual inductance (or slightly less, since it is moving at some constant velocity). But the current is induced in the coil after a delay of only x/c. So his (implied) question is "where did the energy go?"

The problem is most simple when the magnet and coil are stationary with respect to each other (and then we can do a Lorentz transform to find the answer for when the magnet is moving at constant velocity WRT the coil). So for now, I will assume the electromagnet is stationary WRT the coil. Now, when the electromagnet is switched on, a wave will be emitted, immediately carrying energy away from the magnet (this doesn't care if the coil is there or not). And if the coil is there, some of the energy will be taken out of the EM field to start moving the charges around the coil.

Now if the electromagnet were moving with some constant velocity WRT the coil, then a similar thing will happen when the switch is flicked on. (i.e. the electromagnet emits a wave of energy). And after a short time, the current through the electromagnet will become approximately constant. So after the delay of x/c, the coil will feel a brief EM wave, then a steady magnetic field that is slowly increasing because the magnet is getting closer to the coil. So after some time, the electromagnet will start feeling resistance due to mutual inductance. From this explanation, there is no problem that initially the coil has an induced current, while the magnet feels no resistance from mutual inductance, because initially, when the switch was turned on, the electromagnet released some energy into the EM field. So the situation satisfies energy conservation.

Edit: WRT means "with respect to" and EM means "electromagnetic". Also I should say, my whole explanation hinges on the assumption that a stationary electromagnet will emit an electromagnetic wave when it is first switched on. I am pretty sure this is right.
 
  • #55
Also, entropy15, you mentioned on the last page about relativity, and how the EM field looks different in different inertial frames. I don't think it has much relevance to the problem we are talking about, but I decided to work out the EM field due to a magnet moving at constant velocity. (This is when there are no other coils, or any other EM fields, apart from that created by the magnet). (Also, I am assuming that in the rest frame of the magnet, there is zero electric field). Let the magnetic field in the rest frame of the magnet be: [itex]B_x \hat{i} + B_y \hat{j} + B_z \hat{k} [/itex] then, in a reference frame moving to the left WRT the rest frame (i.e. according to an observer who sees the magnet moving to the right):
[tex]\vec{E} = v \gamma (B_y \hat{i} - B_x \hat{j}) [/tex]
(where v is the absolute value of the speed, and I'm guessing you know what gamma is?) Also, the magnetic field is:
[tex]\vec{B} = \gamma(B_x \hat{i} + B_y \hat{j}) + B_z \hat{k} [/tex]
So (assuming that I calculated correctly), even though there is zero electric field in the rest frame, there is a non-zero electric field in this frame where the magnet is moving at constant velocity. Also, the magnetic field has been 'stretched' in both directions perpendicular to the direction of motion. But the magnetic field in the direction of motion remains unchanged.

Aaanyway, as I said, I don't think these equations are much use to the problem we are talking about.
 
  • #56
BruceW said:
So his (implied) question is "where did the energy go?"

You got me right, Bruce. That was what I was trying to say.

BruceW said:
Now, when the electromagnet is switched on, a wave will be emitted, immediately carrying energy away from the magnet (this doesn't care if the coil is there or not). And if the coil is there, some of the energy will be taken out of the EM field to start moving the charges around the coil.

When the electromagnet is switched on, a magnetic field is also set up around it.
At time x/c the effect of this magnetic field reaches the coil. - (since nothing travels faster than light)

Now since the electromagnet is moving at a constant velocity v, there would be change in the magnetic flux linking the coil. Hence there would also be a current induced.

Now I think we can say that the change in the flux linking the coil would be more if the electromagnet was moving more fast. Hence more the induced current.

So let's see what happens between the time interval x/c and the time the electromagnet faces resistance due to mutual induction. This will be less
than 2x/c since it is moving towards the coil.

If the electromagnet was moving with a large velocity we can expect a large change in flux and hence the current induced.

But the energy of the wave emitted by the electromagnet (initially when it is switched on) is independent of this velocity. So how does it account for the large current induced in the coil.

I believe that energy is always conserved. The only thought was that the initial resistance faced by the electromagnet (as soon as it is switched on )was dependent on
whether there is any coil in the vicinity.
 
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  • #57
entropy15 said:
But the energy of the wave emitted by the electromagnet (initially when it is switched on) is independent of this velocity.
This is not correct. I am not certain why you would think this, but it is wrong. Not only is it dependent on the velocity, it is also dependent on the angle of approach. This is called the Doppler effect (see http://en.wikipedia.org/wiki/Relativistic_Doppler_effect). In the forward direction the wave will be blue-shifted and therefore have a higher energy than in the reverse direction where it will be red-shifted. Thus the energy of the wave is higher in the region where the change in flux is higher.
 
  • #58
DaleSpam said:
This is not correct. I am not certain why you would think this, but it is wrong. Not only is it dependent on the velocity, it is also dependent on the angle of approach. This is called the Doppler effect

The total energy due to the radiation in all directions should be independent of velocity.
Isn't that so? Otherwise an electromagnet moving at a non zero velocity will emit more than an electromagnet at rest. (when they are switched on)
 
  • #59
entropy15 said:
The total energy due to the radiation in all directions should be independent of velocity.
The total energy due to the radiation in all directions is not relevant here, only the energy in the direction of the loop, which is higher.

entropy15 said:
Isn't that so? Otherwise an electromagnet moving at a non zero velocity will emit more than an electromagnet at rest. (when they are switched on)
Due to relativistic effects a moving electromagnet will emit more total energy than an electromagnet at rest. Energy is frame variant.
 
  • #60
DaleSpam said:
Due to relativistic effects a moving electromagnet will emit more total energy than an electromagnet at rest. Energy is frame variant.


The energy in the radiation should be coming from the source driving the electromagnet.
Assume that the electromagnet is powered by a power source - a battery or a charged capacitor.

Now if the electromagnet is moving more and more faster (at a constant velocity) does it mean that the source has to provide more and more energy to power on the electromagnet?
 
  • #61
entropy15 said:
The energy in the radiation should be coming from the source driving the electromagnet.
Assume that the electromagnet is powered by a power source - a battery or a charged capacitor.
The energy in the radiation also comes from the KE of the source. When a capacitor is discharged to power the magnet then by E=mc² that capacitor has less mass. So in a frame where it is moving it also has less KE. So not only is the electrical potential energy in the capacitor decreased, but also the KE of the capacitor is decreased. That additional energy goes into the radiation.*

Note that this is a very small effect for ordinary speeds. It is only significant at large fractions of c.

*this explanation is a little sloppy, a better explanation would be in terms of the four-momentum. If you are interested, please open a new thread in the relativity sub-forum.
 
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  • #62
DaleSpam said:
Note that this is a very small effect for ordinary speeds. It is only significant at large fractions of c.

So for smaller velocities (compared to c) there should be no noticeable increase in the amount of energy being emitted by the electromagnet whether it is stationary or moving.

So assume that the velocity of the electromagnet involved in the experiment I mentioned earlier (post 56) is small compared to c.
But it is moving so as to cause a significant change in the flux linking the coil. Then how do we we explain it?
 
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  • #63
Doppler. The total energy is not significantly affected for v<<c, but it is still concentrated in the forward direction. As I said in 59 above, the total energy is not terribly important in this scenario, only the energy at the loop.
 
  • #64
DaleSpam said:
Doppler. The total energy is not significantly affected for v<<c, but it is still concentrated in the forward direction. As I said in 59 above, the total energy is not terribly important in this scenario, only the energy at the loop.

What if we increase the number of turns in the coil? Would that not mean the coil acquiring more energy?
 
  • #65
entropy15 said:
What if we increase the number of turns in the coil? Would that not mean the coil acquiring more energy?
What do you think? Try to reason this from what you know of Maxwell's equations, especially the fact that energy is conserved in them and the fact that they are linear (superposition).
 
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  • #66
DaleSpam said:
What do you think? Try to reason this from what you know of Maxwell's equations, especially the fact that energy is conserved in them and the fact that they are linear (superposition).

Sorry I am unable to think of any reason here. Could you please explain
 
  • #67
Superposition means that if you have two sources then the total field is the sum of the field from each of the two individual sources. Think how that might apply to increasing the number of turns.
 
  • #68
DaleSpam said:
Superposition means that if you have two sources then the total field is the sum of the field from each of the two individual sources. Think how that might apply to increasing the number of turns..

I was referring to the turns in the absorbing coil placed at a distance x from the electromagnet.
 
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  • #69
Me too. Think about the field generated by the induced current in the first turn. How does that affect the total field seen by the second turn.
 
  • #70
DaleSpam said:
Doppler. The total energy is not significantly affected for v<<c, but it is still concentrated in the forward direction. As I said in 59 above, the total energy is not terribly important in this scenario, only the energy at the loop.

The point I was trying to make was that the initail energy due to the current induced in the coil is entirely due to the electromagnetic wave.
The kinetic energy of the electromagnet cannot contribute to the induced current, as it does not decrease initailly.

Lets consider the time interval between x/c and when the coil begins to feel resistance due to mutaul induction. It will be less than 2x/c since the electromagnet is moving towards the coil.
The energy due to the current in the coil during this time cannot be greater than the energy in the electromagnetic wave intially radiated.

But if we increase the value of v, the energy in the coil increases because of a larger change in flux. But there is no noticeable increase in the radiation energy. (v<<c)

If we consider the frame of the moving electromagnet there is no Doppler effect.
All the electromagnet sees is the coil moving towards it.
Here again we can see that the energy in the coil (between x/c and 2x/c) increases with increase in the relative velocity.
 
<h2>1. What is electromagnetic induction?</h2><p>Electromagnetic induction is the process of generating an electric current in a conductor by varying the magnetic field around it. This is achieved by either moving the conductor through a stationary magnetic field or by varying the magnetic field through the conductor.</p><h2>2. How does energy transfer occur in electromagnetic induction?</h2><p>Energy transfer in electromagnetic induction occurs through the conversion of magnetic energy into electrical energy. As the magnetic field changes, it induces an electric field in the conductor, causing the free electrons in the conductor to move and generate an electric current.</p><h2>3. What factors affect the amount of energy transferred in electromagnetic induction?</h2><p>The amount of energy transferred in electromagnetic induction is affected by the strength of the magnetic field, the speed at which the conductor moves or the magnetic field changes, and the properties of the conductor such as its length and material.</p><h2>4. What are some practical applications of electromagnetic induction?</h2><p>Electromagnetic induction has many practical applications, such as in generators and transformers for generating and transmitting electricity, in motors for converting electrical energy into mechanical energy, and in induction cooktops for heating food using a magnetic field.</p><h2>5. How is electromagnetic induction related to Faraday's law and Lenz's law?</h2><p>Faraday's law states that the induced electromotive force (EMF) in a closed loop is directly proportional to the rate of change of the magnetic flux through the loop. Lenz's law states that the direction of the induced current in a conductor will be such that it opposes the change that caused it. Both of these laws play a crucial role in understanding and predicting the behavior of electromagnetic induction.</p>

1. What is electromagnetic induction?

Electromagnetic induction is the process of generating an electric current in a conductor by varying the magnetic field around it. This is achieved by either moving the conductor through a stationary magnetic field or by varying the magnetic field through the conductor.

2. How does energy transfer occur in electromagnetic induction?

Energy transfer in electromagnetic induction occurs through the conversion of magnetic energy into electrical energy. As the magnetic field changes, it induces an electric field in the conductor, causing the free electrons in the conductor to move and generate an electric current.

3. What factors affect the amount of energy transferred in electromagnetic induction?

The amount of energy transferred in electromagnetic induction is affected by the strength of the magnetic field, the speed at which the conductor moves or the magnetic field changes, and the properties of the conductor such as its length and material.

4. What are some practical applications of electromagnetic induction?

Electromagnetic induction has many practical applications, such as in generators and transformers for generating and transmitting electricity, in motors for converting electrical energy into mechanical energy, and in induction cooktops for heating food using a magnetic field.

5. How is electromagnetic induction related to Faraday's law and Lenz's law?

Faraday's law states that the induced electromotive force (EMF) in a closed loop is directly proportional to the rate of change of the magnetic flux through the loop. Lenz's law states that the direction of the induced current in a conductor will be such that it opposes the change that caused it. Both of these laws play a crucial role in understanding and predicting the behavior of electromagnetic induction.

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