The rate of change in the magnetic field linkage in a coil

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Discussion Overview

The discussion revolves around the concepts of magnetic flux linkage and the behavior of a coil rotating in a uniform magnetic field. Participants explore the relationship between the orientation of the coil and the rate of change of magnetic flux, addressing specific phrases that describe these phenomena.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that the rate at which the coil intercepts magnetic field lines is maximum when the coil is parallel to the magnetic flux, while the rate of change of magnetic flux linkage is zero in the same orientation.
  • One participant argues that any maximum of a smooth function has a derivative of zero, suggesting a mathematical relationship between the two statements.
  • Another participant expresses confusion and requests a non-mathematical explanation, leading to a discussion about the inherent mathematical nature of the topic.
  • Some participants assert that the claim regarding the rate of change of magnetic flux linkage being zero when the coil is parallel to the magnetic field is incorrect, referencing a diagram from a previous discussion.
  • There is a discussion about the angle between the velocity of the conductor and the magnetic field when the loop is parallel, with participants agreeing that it is 90 degrees.
  • One participant states that the motional emf induced in the conductor is maximum at 90 degrees and decreases as the angle approaches zero, which is presented as a reason for the incorrectness of the second phrase.
  • Another participant concludes that the first phrase is correct, while the second phrase can be modified to state that the rate of change of magnetic flux linkage equals zero when the plane of the coil is perpendicular to the magnetic field.

Areas of Agreement / Disagreement

Participants express disagreement regarding the correctness of the second phrase, with some asserting it is incorrect while others propose a modified version. There is general agreement on the correctness of the first phrase, but the discussion remains unresolved regarding the implications of the two phrases.

Contextual Notes

The discussion includes various assumptions about the mathematical relationships involved and the definitions of terms like "flux linkage" and "motional emf." Some participants reference diagrams and previous discussions, which may affect the clarity of the current conversation.

Asmaa Mohammad
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Hi,
I would appreciate it if someone explains the difference between these two phases regarding a coil rotates in a uniform magnetic field.
1. The rate with which the coil intercepts the lines of magnetic field in the dynamo is maximum when the plane of the coil is parallel to the lines of the magnetic flux.

2. The rate of change of magnetic flux linkage with a coil rotating in a uniform magnetic field equals zero when the plane of the coil is parallel to the magnetic field.

Why in first case we had maximum value of the ratio and in the second case we get zero?
 
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This is not specific to magnetic flux. Any time you have a maximum of any smooth function the derivative is zero.
 
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Sorry, but I can't say that I understood clearly, please give me more explanation, and let's keep far away from the mathematical point of view.
 
Asmaa Mohammad said:
let's keep far away from the mathematical point of view.
I can't do that. The answer to your question is inherently mathematical. I can explain the math further, but I cannot keep away from it.
 
Last edited:
Asmaa Mohammad said:
The rate of change of magnetic flux linkage with a coil rotating in a uniform magnetic field equals zero when the plane of the coil is parallel to the magnetic field.
This is incorrect. See the diagram I posted in a recent thread of yours about the same topic.
 
Dale said:
I can't do that. The answer to your question is inherently mathematical. I can explain the math further, but I cannot keep away from it.
Oh, ok, let's see how will be this.
 
cnh1995 said:
This is incorrect. See the diagram I posted in a recent thread of yours about the same topic.
Yes, I remember the point we discussed about the flux linkage to the coil.
We said the flux through the coil is zero when it is parallel, right?
 
Asmaa Mohammad said:
Yes, I remember the point we discussed about the flux linkage to the coil.
We said the flux through the coil is zero when it is parallel, right?
Right.
 
Ok then, why phrase 2 is incorrect?
 
  • #10
Asmaa Mohammad said:
Ok then, why phrase 2 is incorrect?
Rate of change of flux is maximum when the flux linkage is zero.
 
  • #11
cnh1995 said:
Rate of change of flux is maximum when the flux linkage is zero.
How is this?
 
  • #12
Asmaa Mohammad said:
How is this?
What is the angle between velocity of the conductor and the magnetic field when the loop is parallel to the magnetic field?
 
  • #13
cnh1995 said:
What is the angle between velocity of the conductor and the magnetic field when the loop is parallel to the magnetic field?
it will be 90 degrees.
 
  • #14
Asmaa Mohammad said:
it will be 90 degrees.
Yes. So what is the motional emf induced in the conductor? How will it vary with respect to this angle?
 
  • #15
cnh1995 said:
Yes. So what is the motional emf induced in the conductor? How will it vary with respect to this angle?
It will be maximum when the angle is 90 degrees.
When the angle decreases the motional emf will decrease too until it becomes zero when the angle between the velocity and the field lines is zero.
 
  • #16
Asmaa Mohammad said:
It will be maximum when the angle is 90 degrees.
When the angle decreases the motional emf will decrease too until it becomes zero when the angle between the velocity and the field lines is zero.
Right. This is why phrase 2 is incorrect.
 
  • #17
cnh1995 said:
Right. This is why phrase 2 is incorrect.
OK, and what about phrase 1?
 
  • #18
Asmaa Mohammad said:
OK, and what about phrase 1?
It is correct. In fact, the rate at which the conductor intercepts magnetic field lines is equal to the rate of change of magnetic flux associated with the loop. The physical situation in both the phrases is same but they contradict each other. Only one of them can be true, and that is phrase 1.
 
  • #19
cnh1995 said:
It is correct. In fact, the rate at which the conductor intercepts magnetic field lines is equal to the rate of change of magnetic flux associated with the loop. The physical situation in both the phrases is same but they contradict each other. Only one of them can be true, and that is phrase 1.
OK, I think I started to understand.
And to make the second phrase correct, we say:
"The rate of change of magnetic flux linkage with a coil rotating in a uniform magnetic field equals zero when the plane of the coil is perpendicular to the magnetic field."
Is this correct?
 
  • #20
Asmaa Mohammad said:
OK, I think I started to understand.
And to make the second phrase correct, we say:
"The rate of change of magnetic flux linkage with a coil rotating in a uniform magnetic field equals zero when the plane of the coil is perpendicular to the magnetic field."
Is this correct?
Yes.
Emf is proportional to the rate of change of flux.
If flux linkage is sinusoidal, the emf is co-sinusoidal (derivative of sine). This is why when flux linkage is zero, emf is maximum and when flux linkage is maximum, emf is zero.
 
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