The EMF induced in straight current-carrying conductor

In summary: Faraday's law states that a moving wire cutting through a uniform magnetic field experiences an induced e.m.f. This e.m.f. is equal to the rate of change of magnetic flux, which is constant in this case due to the wire's constant area and magnetic flux density. However, for a coil already in the magnetic field and moving the same way, no e.m.f. is induced. This is because the coil has two sides and the induced e.m.f. in each side opposes each other. This is different from a straight current carrying conductor, where the induced e.m.f. is in the same direction. The Lorentz force law is the relevant law to consider in this case.
  • #1
funmi
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Why is an emf induced in straight current carrying conductor as it moves at at right angles to a uniform and constant magnetic filed. By Faraday's law, this e.m.f. is equal to dΦ/dt but I do not understand how a wire cutting a uniform magnetic field experiences a change in magnetic flux . Its area is constant and magnetic flux density is constant so the magnetic flux felt by the wire Φ=BA is constant.

Wire-cutting-a-magnetic-field.png

Wire(green) is moving down at right angles to the field
 
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  • #2
Google "Lorentz force"

And indicate the direction of motion of the wire in the drawing
 
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  • #3
Faraday's law can be written as:
emf = d/dt BAN
Assume B is constant and N =1 we can write:
emf = B dA/dt
In this example dA/dt is the rate of change of area in other words the area sliced out by the wire in one second. If the wire has length l and is moving up or down with velocity v the area sliced out per second will be lv. Make a sketch and hopefully you will see it.
 
  • #4
Dadface said:
Faraday's law can be written as:
emf = d/dt BAN
Assume B is constant and N =1 we can write:
emf = B dA/dt
In this example dA/dt is the rate of change of area in other words the area sliced out by the wire in one second. If the wire has length l and is moving up or down with velocity v the area sliced out per second will be lv. Make a sketch and hopefully you will see it.
but this doesn't work for a coil, if i replaced the straight wire with a coil already in the magnetic field and moved it the same way with no rotation no emf would be induced. why is it different for a coil and a straight current carrying conductor
 
  • #5
Perhaps because the coil has two sides and the emf in each side opposes when they both move in the same direction.
induction.png
 
  • #6
funmi said:
By Faraday's law, this e.m.f. is equal to dΦ/dt but I do not understand how a wire cutting a uniform magnetic field experiences a change in magnetic flux . Its area is constant and magnetic flux density is constant so the magnetic flux felt by the wire Φ=BA is constant.
Well, there isn’t really a loop here, so Faraday’s law doesn’t really make a difference in this case. If you make the “loop” with zero area by going backwards and forwards along the same line then by Faraday’s law you get 0 EMF and any voltage distribution along the wire is consistent with 0 EMF since you will go forwards and backwards across the same distribution. So basically, you need to look for a different law.

The law to look at is the Lorentz force law.
funmi said:
if i replaced the straight wire with a coil already in the magnetic field and moved it the same way with no rotation no emf would be induced.
That is correct. No EMF is induced in such a coil moving through a uniform magnetic field.
 
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  • #7
For a closed loop moving at steady velocity within a uniform B field there will be no internal current but, as predicted by the Lorentz law, there will be a build up of electrons, most concentrated at one end of the loop, and a shortage of electrons, most concentrated at the other end. Hence there will be an emf. A current can be drawn by adding external circuitry eg a piece of wire connected to the ends of the loop.
 
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  • #8
Dadface said:
Hence there will be an emf.
Not around the whole loop. The EMF on one side cancels out the EMF on the other for a total of 0 EMF around the loop.
 
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  • #9
Dale said:
Well, there isn’t really a loop here, so Faraday’s law doesn’t really make a difference in this case. If you make the “loop” with zero area by going backwards and forwards along the same line then by Faraday’s law you get 0 EMF and any voltage distribution along the wire is consistent with 0 EMF since you will go forwards and backwards across the same distribution. So basically, you need to look for a different law.

The law to look at is the Lorentz force law.That is correct. No EMF is induced in such a coil moving through a uniform magnetic field.
Thank you I think I understand, just to clarify I can make a "loop" while moving the wire forward and backward( to make the loop) as I move it up and down between the magnets, it will produce no emf because the direction of the current will be the same as wire's movement whether forward or backward.
 
  • #10
Dadface said:
For a closed loop moving at steady velocity within a uniform B field there will be no internal current but, as predicted by the Lorentz law, there will be a build up of electrons, most concentrated at one end of the loop, and a shortage of electrons, most concentrated at the other end. Hence there will be an emf. A current can be drawn by adding external circuitry eg a piece of wire connected to the ends of the loop.
Thanks
 
  • #11
funmi said:
I can make a "loop" while moving the wire forward and backward( to make the loop)
Not exactly. In this context a "loop" is a closed path at a given moment in time. So if you have to spend time to make a closed path then it isn't a "loop" in the meaning of this law.

There are other contexts where the sort of loop you are describing is perfectly acceptable, such as describing the work done on a point particle moving in a conservative force field, but in Maxwell's equations the surface and loop integrals are at a given instant of time. Those loops can change over time, either by stretching or moving, but at every moment they are a complete closed path.
 

Related to The EMF induced in straight current-carrying conductor

1. What is the concept of EMF induction in a straight current-carrying conductor?

The concept of EMF (electromotive force) induction in a straight current-carrying conductor refers to the phenomenon where an electric current is induced in a conductor when it is exposed to a changing magnetic field. This is governed by Faraday's law of induction, which states that the magnitude of the induced EMF is directly proportional to the rate of change of the magnetic flux through the conductor.

2. How is the direction of the induced EMF determined in a straight current-carrying conductor?

The direction of the induced EMF in a straight current-carrying conductor is determined by Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic flux that caused it. This means that the induced current will create a magnetic field that opposes the external magnetic field, and this can be used to determine the direction of the induced EMF.

3. What factors affect the magnitude of the induced EMF in a straight current-carrying conductor?

The magnitude of the induced EMF in a straight current-carrying conductor is affected by several factors, including the strength of the external magnetic field, the rate of change of the magnetic field, and the length and orientation of the conductor. Additionally, the material and resistance of the conductor can also impact the magnitude of the induced EMF.

4. Can the induced EMF in a straight current-carrying conductor be increased?

Yes, the induced EMF in a straight current-carrying conductor can be increased by increasing the strength or rate of change of the external magnetic field, or by changing the orientation of the conductor. Additionally, using a material with lower resistance or increasing the length of the conductor can also increase the induced EMF.

5. What are some practical applications of the concept of EMF induction in straight current-carrying conductors?

The concept of EMF induction in straight current-carrying conductors has many practical applications, including power generation in electric generators, transformers, and induction motors. It is also used in devices such as metal detectors, magnetic levitation trains, and induction cooktops. Additionally, EMF induction is used in wireless charging technology and in various medical devices such as MRI machines.

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