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

[Asmaa Mohammad]

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?

 

[Dale]

This is not specific to magnetic flux. Any time you have a maximum of any smooth function the derivative is zero.

 

[Asmaa Mohammad]

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.

 

[Dale]

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.

 

[cnh1995]

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.

 

[Asmaa Mohammad]

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.

 

[Asmaa Mohammad]

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?

 

[cnh1995]

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.

 

[Asmaa Mohammad]

Ok then, why phrase 2 is incorrect?

 

[cnh1995]

Ok then, why phrase 2 is incorrect?

Rate of change of flux is maximum when the flux linkage is zero.

 

[Asmaa Mohammad]

Rate of change of flux is maximum when the flux linkage is zero.

How is this?

 

[cnh1995]

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?

 

[Asmaa Mohammad]

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.

 

[cnh1995]

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?

 

[Asmaa Mohammad]

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.

 

[cnh1995]

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.

 

[Asmaa Mohammad]

Right. This is why phrase 2 is incorrect.

OK, and what about phrase 1?

 

[cnh1995]

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.

 

[Asmaa Mohammad]

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?

 

[cnh1995]

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.