Trace on the screen of a C.R.O. when a deflection coil is rotated

[songoku]

Homework Statement

Large flat circular coil connected to a sinusoidal alternating voltage supply and a small flat circular coil placed at the centre of the large coil such that the planes of the two coils are coincident. The smaller coil is connected to a cathode – ray oscilloscope (c.r.o). State and explain how the trace on the screen of the c.r.o. would be affected if the small coil is rotated such that the angle between the planes of the two coils increases from zero to 90 degrees whilst maintaining a constant root mean square current in the large coil

Relevant Equations

Faraday's Law

My answer is when the small coil is rotated, there will be change in magnetic flux in it. Initially (before rotated), the trace in c.r.o will be sinusoidal. After it is rotated, the trace will still be a sinusoidal (but I am not sure whether the amplitude will be the same).

But the answer key is: the trace will go down to zero since when the angle is 90 degrees no field lines passing through the area of small coil so the magnetic flux is zero.

I don't understand why the trace will go down to zero.

Thanks

 

[BvU]

Hi,

I am not sure whether the amplitude will be the same

Your hunch is good. So: what is it that determines the amplitude of the emf induced in the small coil ?

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[songoku]

Hi,

Your hunch is good. So: what is it that determines the amplitude of the emf induced in the small coil ?

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Based on Faraday's Law, the magnitude of emf depends on rate of change of magnetic flux so in this case it depends on how fast the small coil is rotated. Since I don't know how fast it is rotated, it means that I can't determine whether the amplitude will be same, smaller or larger?

Thanks

 

[Lnewqban]

When the small coil is relocated to be perpendicular to the paper (quickly or slowly), how does it feel the lines of the alternating magnetic field created by the big coil still parallel to the paper?

 

[BvU]

Based on Faraday's Law, the magnitude of emf depends on rate of change of magnetic flux so in this case it depends on how fast the small coil is rotated. Since I don't know how fast it is rotated, it means that I can't determine whether the amplitude will be same, smaller or larger?

Thanks

very good point, but we may asssume the exercise is meant to be pretty elementary.

For starters, assume it's rotated very slowly...

 

[songoku]

When the small coil is relocated to be perpendicular to the paper (quickly or slowly), how does it feel the lines of the alternating magnetic field created by the big coil still parallel to the paper?

very good point, but we may asssume the exercise is meant to be pretty elementary.

For starters, assume it's rotated very slowly...

While rotating, it will experience change in magnetic field but the change will be smaller compared to initial position so the amplitude of emf will be smaller, finally the amplitude will be zero when the planes of the coil are perpendicular to each other? Is this what the question meant by the trace will go down to zero?

Thanks

 

[BvU]

Correct !

 

[songoku]

Sorry @Lnewqban and @BvU , but I have another question. For this second question, I got the answer correctly, which is (B). In this question, when the plane of the loop is parallel to magnetic field, the flux is zero but the induced current (hence induced emf) is maximum since the rate of change of magnetic flux is maximum.

But for question in post#1, when the plane of small coil is parallel to the magnetic field produced by large coil, the emf goes down to zero. I feel like my explanation for these two questions contradict each other

What am I missing?

Thanks

 

[BvU]

In the exercise in post #1 the field from the outer coil is changing rapidly and (for the exercise) the change in orientation of the inner coil (by rotation, e.g. manually) is supposed to go a lot slower.

In the exercise in post #8 the magnetic field is constant and the only source of emf is the change in orientation of the coil.

It does you credit that you approach the first exercise with an open mind -- and thereby made it difficult for yourself -- something the exercise composer should have thought of, and could have avoided by mentioning something like 'is rotated slowly'

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[songoku]

Thank you very much for the help and explanation BvU and Lnewqban