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

Tags:
1. Jun 6, 2017

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?

2. Jun 6, 2017

### Staff: Mentor

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

3. Jun 6, 2017

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.

4. Jun 6, 2017

### Staff: Mentor

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: Jun 6, 2017
5. Jun 6, 2017

### cnh1995

This is incorrect. See the diagram I posted in a recent thread of yours about the same topic.

6. Jun 6, 2017

Oh, ok, let's see how will be this.

7. Jun 6, 2017

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?

8. Jun 6, 2017

### cnh1995

Right.

9. Jun 6, 2017

Ok then, why phrase 2 is incorrect?

10. Jun 6, 2017

### cnh1995

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

11. Jun 6, 2017

How is this?

12. Jun 6, 2017

### cnh1995

What is the angle between velocity of the conductor and the magnetic field when the loop is parallel to the magnetic field?

13. Jun 6, 2017

it will be 90 degrees.

14. Jun 6, 2017

### cnh1995

Yes. So what is the motional emf induced in the conductor? How will it vary with respect to this angle?

15. Jun 6, 2017

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. Jun 6, 2017

### cnh1995

Right. This is why phrase 2 is incorrect.

17. Jun 6, 2017

OK, and what about phrase 1?

18. Jun 6, 2017

### cnh1995

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. Jun 6, 2017

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. Jun 6, 2017

### cnh1995

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.