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Energy transfer in electromagnetic induction

by entropy15
Tags: electromagnetic, energy, induction, transfer
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entropy15
#73
Jan8-13, 08:05 AM
P: 37
Quote Quote by Jano L. View Post
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..
You mean to say that there is limit to the energy that can be transferred to the coil between the interval x/c and 2x/c.

Can we not increase the energy transferred initially by increasing the number of turns in the coil. More turns mean more current flowing in the coil.
BruceW
#74
Jan8-13, 10:17 AM
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This goes back to the point before. I think DaleSpam's answer was: "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. My hint is that the equation:
[tex]\displaystyle{\varepsilon}=-N \frac{d \Phi}{dt} [/tex]
Uses a lot of assumptions, and if you break those assumptions, you cannot expect the equation to give correct results.

Edit: actually, it doesn't use a lot of assumptions, but the simple case of increasing number of turns to increase the current through the coil does introduce assumptions.

Another Edit: and generally, it is assumptions used along with this equation that have caused the problems in this thread. For example, the assumption "that the magnetic field at the magnet and at the coil is approximately the same" is often used with this equation, but this assumption becomes false when the magnet and coil are far away from each other.
DaleSpam
#75
Jan8-13, 10:54 AM
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Quote Quote by entropy15 View Post
You mean to say that there is limit to the energy that can be transferred to the coil between the interval x/c and 2x/c.

Can we not increase the energy transferred initially by increasing the number of turns in the coil.
In addition to BruceW's point above, I would like to point out that the two statements are not mutually exclusive. Specifically, it is possible that the statements "there is a limit to the energy that can be transferred" and "we can increase the energy transferred by increasing the number of turns" can both be true.
entropy15
#76
Jan8-13, 11:09 AM
P: 37
Quote Quote by DaleSpam View Post
In addition to BruceW's point above, I would like to point out that the two statements are not mutually exclusive. Specifically, it is possible that the statements "there is a limit to the energy that can be transferred" and "we can increase the energy transferred by increasing the number of turns" can both be true.
How is that possible?
DaleSpam
#77
Jan8-13, 01:05 PM
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Quote Quote by entropy15 View Post
How is that possible?
Like this (ignore the scale and units of the vertical axis, this is just to give a general idea of the concept of a monotonically increasing function with a horizontal asymptote)

If each dot represents the energy extracted by a coil with i turns then it is both true that "there is a limit to the energy that can be transferred" and "we can increase the energy transferred by increasing the number of turns".
entropy15
#78
Jan9-13, 11:56 AM
P: 37
Quote Quote by DaleSpam View Post
Like this (ignore the scale and units of the vertical axis, this is just to give a general idea of the concept of a monotonically increasing function with a horizontal asymptote)
Thanks for clarifying. This seems to indicate that the amount of energy transferred converges to a fixed value as N (no. of turns) tends to infinity.

Is this because the successive turns in the coil are linked to lesser magnetic flux?
DaleSpam
#79
Jan9-13, 12:39 PM
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Yes, it is because each turn reduces the flux seen by the other turns. This can be seen through the superposition principle.

Suppose that you have two turns, consider them to be two separate loops. There is a current in loop A which creates a field which opposes the change in the external field. By superposition the field seen by loop B is the sum of the field from loop A and the external field, which is less than the change in the external field. So the current induced in B is a function of the external field and the current induced in A where current in A reduces the induced current in B.

Then, to consider the loops as separate turns in a single coil simply equate the current in A to the current in B.


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