Why is the Voltage Induced in a Rotating Coil Sinusoidal?

[souky101]

Sinusoidal wave form ?

I am asking:

We know that if a coil rotates in a transverse magnetic field a sinusoidal voltage is induced between its terminals.

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My question now is:

Why it is exactly sinusoidal in the shape and not any other wave shape??

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[FactChecker]

Sine waves are fundamental to the physics of rotating objects. The sine wave is the basic description of a position on a rotating object. Whether you are talking about the distance of a point on the rotating object to some other place, its x-coordinate position, or its y-coordinate position, they will all have a sine wave in one form or another. Furthermore, the velocities and accelerations of a point on a constantly rotating object can be expressed with sine waves in some way.

 

[souky101]

If we look at the automotive alternator we find a rotating field ( produced by 2 poles -North and south) and stator conductor is stationary.
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Is the magnetic flux passes from the North pole to the south pole has a half wave of a sinusoidal shape - and that is why we get induced voltage of a sinusoidal shape ??

 

[FactChecker]

Yes.

 

[souky101]

Is the flux lines crossing from the North pole to the South pole have exactly "half wave shape" of a prefect sinusoidal wave form ??
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Do you have any reference supports that thought? / guessing??

 

[FactChecker]

An educated guess. If you want a proof that works in all situations, I recommend these steps:
1) prove that the sum of sines of the same period gives a sine of that period. That would be a basic trig fact.
2) prove that a single wire going in a circle in a magnetic field gives a sine. The fact that position and velocity components are sine functions should help.
3) show that any combination of wires and magnetic fields can be described as the sum of outputs from a single wire in a single magnetic field. This should follow from the fact that fields are additive.

I haven't looked for a reference, but I think you might find one with Google.

 

[souky101]

My question again in simplified way :

Is the magnetic flux passes from the North pole to the south pole of a magnet consists of group of " half waves of a perfect sinusoidal shape' with different amplitudes ?

 

[FactChecker]

My question again in simplified way :

Is the magnetic flux passes from the North pole to the south pole of a magnet consists of group of " half waves of a perfect sinusoidal shape' with different amplitudes ?

When you get down to that basic question, I am not sure of the answer. I guess that I would be surprised if it was always a perfect sine wave in all situations -- for all shapes of magnets. But it still might be true. I will have to leave it to someone more expert in that subject.