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Energy transfer in electromagnetic induction 
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#55
Jan613, 06:02 PM

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P: 3,443

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 nonzero 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
Jan713, 01:24 AM

P: 37

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 lets 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. 


#57
Jan713, 05:06 AM

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#58
Jan713, 06:17 AM

P: 37

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
Jan713, 06:36 AM

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#60
Jan713, 07:40 AM

P: 37

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
Jan713, 07:52 AM

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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 fourmomentum. If you are interested, please open a new thread in the relativity subforum. 


#62
Jan713, 08:32 AM

P: 37

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? 


#63
Jan713, 08:53 AM

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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
Jan713, 09:07 AM

P: 37




#65
Jan713, 09:18 AM

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#66
Jan713, 01:40 PM

P: 37




#67
Jan713, 02:06 PM

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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
Jan713, 02:25 PM

P: 37




#69
Jan713, 03:04 PM

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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
Jan813, 02:56 AM

P: 37

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. 


#71
Jan813, 06:50 AM

PF Gold
P: 1,150

What is important, is that in the frame of the coil, the electromagnet is moving towards it. When a source of isotropic radiation moves in some direction, the radiation is released preferentially to that direction. Check https://en.wikipedia.org/wiki/Synchrotron_radiation The bunches of charged particles circling in synchrotron move so fast that the radiation is needlelike, similar to laser, only much brighter and not monochromatic. With the electromagnet, it is similar; even if it moves slowly, there is more radiation going to the coil than in the other directions. As the velocity is increased, coil receives greater and greater power. However, there is a limit: when v approaches c, the coil receives almost all the radiated power 1 J/s and this is the maximum. Of course, as the processes in the source are slowed down (dilatation) , it will receive it for a long time and thus the net amount of energy received in the end can be much greater than 1 J. Where did the extra energy came from? From the total energy of the electromagnet; as the net energy of the electromagnet decreases by radiation, in the frame of the coil the electromagnet loses also momentum via loss of its mas (the velocity is unaffected). 


#72
Jan813, 07:08 AM

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