Electromagnetic induction

  1. E= -N [tex]\frac{d\phi_{B}}{dt}[/tex]

    Does this formula apply to any type of wire? If so, how?

    It simply doesn't make sense to me that a magnetic field acting on a coil of copper would induce the same emf as if it was a coil, for instance, of aluminium.
  2. jcsd
  3. jtbell

    Staff: Mentor

    The induced EMF (volts) is the same no matter what the coil is made of. The induced current (amps) depends on the resistance of the coil via V = IR.
  4. You don't even need a wire! You can define a two dimensional area in vakuum and the law will still be valid. Example is the propagation of light, where electric field is induced by time dependent magnetic field (and vice versa).
  5. I still don't get it...

    How can a magnetic field acted on any material induce the same emf? If we take a look at the atomic structure/electrons configuration there are materials which need a higher force to move free electrons than other materials, in order to produce an emf, right? If so, how does the same magnetic field strength induce the same emf in whatever material?
  6. Maybe you are trying to find analogy in electrostatic induction, where primary electric field changes distribution of charge in a conductor and that charge then causes secondary electric field.

    This analogy is completely invalid for induced electric field (caused by change of magnetic field)!

    The time dependent magnetic field does not move any charge to induce electric field. Like I said before: this principle works even in vakuum, where there are no charges. It is a basic law of nature and does not need any proof (except for consistency with experiments).
    Last edited: Feb 25, 2008
  7. Not to be confrontational, but are you sure about that?

    If a time changing magnetic flux cuts through a coil, with the terminals shorted, what happens? If the coil is wound with very high resistance wire, a low current is induced, and a voltage. If the resistance is increased further, the voltage converges to a maximum limit, and the current decreases. As the wire resistance is reduced, the current increases to an extent and the voltage decreases. When the resistance is near zero, the voltage is decreased, and the current converges to an asymptotic limit.

    I'm presuming that the coil is closed upon itself. Is that what the the OP is telling us?

    Electromagnetic induction is neither "constant-current" nor "constant-voltage".
  8. The action of induction is constant as explained earlier. However changes in observation are the result of particular circuit properties not different induction properties. And the same calculations are employed. Coil resistance will affect the amount of current that can flow from the induced EMF and therefore can affect the power pulled from a coil but has nothing to do with induction.
  9. Perhaps I can help you with that.

    If you have even a high resistance winding cutting a magnetic field and it is open you will read exactly the same voltage as a low resistance winding. When you short the terminals of a coil with a wire across it and you measure the terminals you will be measuring the voltage drop of the wire shorting it.

    The difference between the coils will be the amount of current that will flow. It fallows ohms law. The resistance of the coil will consume power and change it to heat. what current you get left will be proportionate to the voltage induced I.E. 10V of EMF will push 10A of current through a 1 ohm coil, and a 1 amp from a 10 ohm coil.

    Hope this clears it up a bit. And show how the material of a coil is independent of the EMF produced
  10. Could you please elaborate as to what you mean by "the action of induction is constant"? Are you inferring constant power, voltage, or current? Induction cannot be constant current or constant voltage. If it was constant voltage, the following results in a paradox. Let's say that for a given flux "phi", changing w/ time, a constant voltage is induced. If the resistance is lowered, current increases. Power is (V^2)/R. If the R is reduced, power is increased. But the incident magnetic field has a specific power associated with it. The power induced into the loop cannot exceed the power in the magnetic field.

    Likewise, if induction was a constant current action, as R increases, power increases indefinitely, at odds with conservation of energy.

    With very low R, constant current source action is approximated. As R decreases the current converges to a limit and the voltage drops. When R increases, there is a point where I decreases and V increases, neither constant-I nor constant-V. Then at some value of R, the action tends towards constant voltage as the V converges to a limit, and I drops as R increases.

    This is well documented. The CEL (conservation of energy law) is inviolate, as well as OL (Ohm's law), FL (Faraday's Law), and AL (Ampere's Law).
  11. You're saying that 10V of emf results in 10A through the 1 ohm coil. But that is 100 watts of power. What if the magnetic field has an incident power of just 1 watt? The induced power cannot exceed the power in the field! Where does this extra power come from?

    As the R is reduced, the larger induced I generates its own magnetic field which opposes the incident field. This field induces an emf which COUNTERS that from the external field. As R is reduced, the voltage across the coil DECREASES.

    Hence, depending on the external field power, when the induced current's magnetic field becomes significant compared with the external field, bucking action takes place, the the NET emf across the coil is reduced.
  12. it sounds like you have a fair knowlage of the subject, so I apologize if I sound as though I am talking down to you, I am afraid I have no other way of explaining things.

    You answered this yourself. The magnetic field of the current flowing counters the magnetic field of the source thereby causing less of the magnetic field to be exposed to the winding. The law still applies; the voltage will still be proportionate to the rate of change of the magnetic field that the conductor is exposed to. It is just that if the magnetic field generated by the coil due to its current overpowers the source field and thus less source field is available for the induction.

    Since I basically said what you did, why is the law in conflict? Fallow the math and you will find that it is constant voltage. if a magnetic field cuts a conductor it will produce an EMF only in proportion of the rate of change and strength of the magnetic field but not the resistance of the conductor or what the conductor is made of.

    As for the "the action of induction is constant" I am not sure what you are getting from this. Constant in context refers to mathematical non-ambiguity; there is no consideration of resistance, power, current, just voltage. Since voltage is a force not energy or power any change in the circuit has to be accounted for and not interpreted as a change in the laws of induction.

    Since you are aware of the documentation I am not sure where the misunderstanding is. It could be semantics I guess so I will fallow the steps logically.

    A magnetic field is setup in a transformer the secondary sees the change in the magnetic field. A voltage is induced. This voltage is directly proportional to the changing magnetic field that it is exposed to. The coil is a high resistance and it is dead shorted. as soon as the rate of the magnetic field reaches the point that the emf overcomes the resistance of the coil and overpowers the primary field the amount of voltage induced levels off until the system is balanced (the voltage induced is still proportional to the rate of change of field, but the field has been reduced so the amount of voltage is also reduced, the voltage is still consistent to the equation)

    Just because the amount of magnetic field available is reduced does not mean that induction is not constant voltage. It just means that the properties of the circuit have changed

    But like I said it sounds like you already know this stuff, forgive me if I am missing the point. I did not claim anything that would violate the laws of conservation or other laws I was just explaining what would happen to your example with what information you gave. Assuming a magnetic field with 100watts of freely available power was not in contention with your example.

    The definition of constant voltage as it would apply to this as far I know it to be:

    An induced emf that cannot be changed with influences outside of the equation such as material, resistance, power, current, starting voltage ect., Which is the subject of the OP.
  13. But my point was that the mag field due to induced current in the coil CANNOT overpower the source field. CEL would be breached.

    As far as the transformer goes, how can the emf "overcome" the resistance? Resistance and emf are differing quantities with differing units, as one cannot overcome the other. Also, "voltage" is NOT "force". Voltage is work per unit charge, or time rate of change of flux. Force is mass times length per time squared. Force and voltage are completely different physical quantities.

    A transformer secondary exhibits "constant voltage" behavior only because it's primary is driven by a constant voltage source (CVS). When the load resistance on the secondary changes, the voltage remains approx. constant, with current varying inversely w/ load resistance. This is due to the CVS nature of the power source driving the primary, NOT the nature of induction. Induction can exhibit behavior which is constant current, constant voltage, or neither. If the transformer primary were driven by a CCS (constant current source), as the secondary load resistance varies, the current would remain approx. constant and the secondary voltage would change in proportion to the resistance. Again, the constant current behavior of the secondary is due to the CCS driving the primary, NOT induction itself.

    Induction is neither CC nor CV. Although the voltage is directly proportional to the time rate of change of the magnetic flux density "B", the current is directly proportional to the magnetic field intensity "H". But "B" and "H" are related via the permeability "mu". All of these actions are mutual and simultaneous.

    To summarize, if the coil is shorted, and has very low resistance, as the resistance is gradually decreased, the current will converge to a limit. As R increases, I barely changes, but the voltage will increase. The behavior is CC. Then the R will increase to the point where V increases and I decreases, neither CC nor CV. Then at a high enough value of R, the voltage will converge to a limit, with current decreasing with increasing R, or CV operation. All the while, the I*V product cannot exceed the power in the external mag field (CEL).

    I hope I've explained it well.
  14. You are right, "the mag field due to induced current in the coil CANNOT overpower the source field"- but that has nothing to do with the equation noted by unseensoul.

    Force causes mass to accelerate, emf is (Electro Motive Force) measured in volts, it may be a misnomer but behaves in much the same way. Voltage is needed to overcome (meaning simply I = V/R) the resistance of a system, and thus have power to do work given time. EMF cannot do work without current and time (work measured in joules as it is reciprocal of energy) I am not the only one that uses the comparison, it was not so long ago and still is in high voltage referred to as pressure, and Nicola Tesla once described his apparatus having such great tension as to incinerate the air with horrible violence, referring to the voltage of his device. And don’t forget high tension power lines; all describing EMF or voltage (not necessarily measured voltage) as a force.

    I think I see the confusion. The equation only describes what is going on with the conductor or coil. Perhaps one can look at it this way. If one has a CVS and adds to it a circuit that varies the voltage according to the load and passes it to an output terminal and one looks at it as a whole then it no longer looks CV. the CVS is still a CVS but the circuit as a whole is not. When looking at a transformer, dynamo, motor, ect. One is looking at the whole system, only part of which is induction.

    "The value of the emf for the battery (or other source) is the value of this 'open circuit' voltage. When the battery is charging or discharging, the emf itself cannot be measured directly. It can, however, be inferred from a measurement of the current I and voltage difference V, provided that the internal resistance has already been measured: I=( -V)/r."
    -wikipedia (EMF)

    Originally Posted by jtbell:
    “The induced EMF (volts) is the same no matter what the coil is made of. The induced current (amps) depends on the resistance of the coil via V = IR.”

    This statement is all I am trying to explain (probably poorly). I am not in contention with power, energy or any other point that you are making. It is simply that the statement made by jtbell is completely true.
  15. If force causes mass to accelerate, why do physicists refer to "F = ma" as "circular"? One cannot define force and mass independently. Are you saying that voltage "causes" current. I certainly hope not, as that has been known not to be the case since the 19th century.

    As far as the original statement goes, I beg to differ. The OP asked if the current is determined by the resistance of the coil and voltage V. I stated that it is not. The equation I = V/R always holds, but the question is whether the induced voltage remains constant as R decreases, which is not what happens. Otherwise I would increase without limit as R is decreased, which does not happen.

    Current I, and voltage V, are *interactive* and *mutually inclusive*. The ratio of V to I is always R, in accordance with Ohm, but we cannot treat "V" as a constant. As R is lowered and I increases, V eventually decreases.

    You said that work is the "reciprocal" of energy. Good grief! Work and energy are equivalent, both measured in joules. There are some severe theory limitations being presented here. I can't spend any more effort explaining. You keep reiterating that which Ampere, Faraday, Lenz, Maxwell and others laid to rest in 1873. I am at a loss to make it clearer.

    The best thing for me to do is to get on my horse and ride off into the sunset.

    Good day to all.
  16. I did not say "the reciprocal" I said "is reciprocal" which means equivalent . I am sorry for the fuss.

    I thought you had a question that needed answering. I did not realize it was rhetorical.

    heh, all this time you were trying to educate me?! I can be thick headed sometimes :smile:

    I meant no frusteration.

  17. Yes.
  18. If so, how is a voltage produced? If a changing magnetic field acts on a material, the electrons of that material are in motion in respect to the magnetic field therefore it will result in a force applied to the electrons forcing them to move in a given direction...this way, a voltage will be produced, or am I wrong?
  19. Go outside tonight. Look at the stars. Are they in a practical vacuum? Are you still able to see their light?
  20. I still can't find a relationship between what you've mentioned and what I've asked... :S
  21. Look up electromagnetic induction on Wiki, there is a good description of what you are asking.

    But if I try and apply it to the OP, EMF is the pressure that the electrons have on them to flow, not the flow its self. You are describing the result of this action. And so, no mater what material it is the magnetic field will induce the same EMF according to your sited math. What the conductor does with the EMF is another story.


    This is the way I understand it anyway.
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