Emf in coil rotating inside magnetic field

AI Thread Summary
The discussion revolves around the confusion regarding the induced electromotive force (emf) in a coil rotating within a magnetic field. The initial claim was that the emf should be non-zero, but it was clarified that the magnetic flux through the coil is indeed zero due to the orientation of the magnetic field relative to the coil. The key point is that induced emf occurs only when there is a change in magnetic flux over time. Since the magnetic field does not pass through the coil during its rotation, the rate of change of magnetic flux is zero, leading to zero induced emf. The participants express gratitude for the clarification on this concept.
songoku
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Homework Statement
Please see below
Relevant Equations
emf = - dφ / dt
1712279767802.png


My answer is (B) but the answer key is (A).

My working:
$$\varepsilon=-\frac{d\phi}{dt}$$
$$=-AB\frac{cos\omega t}{dt}$$
$$=AB\omega \sin \omega t$$

Why the answer is zero? I thought the flux will be zero, not the emf.

Thanks
 
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songoku said:
Why the answer is zero? I thought the flux will be zero, not the emf.
How much of the magnetic field ##B## is normal to the area ##A##?
 
Look at the deifiniton for flux. ##\Phi=(\mathbf B\cdot\mathbf{\hat n})~A## where ##\mathbf {\hat n}## is perpendicular to the plane of the coil. As you say, the flux is zero. You get an induced emf if the flux changes with time. Does it?
 
renormalize said:
How much of the magnetic field ##B## is normal to the area ##A##?
kuruman said:
Look at the deifiniton for flux. ##\Phi=(\mathbf B\cdot\mathbf{\hat n})~A## where ##\mathbf {\hat n}## is perpendicular to the plane of the coil. As you say, the flux is zero. You get an induced emf if the flux changes with time. Does it?
Ah I see. Seeing the rotation of the coil with respect to magnetic field, there won't be any B passing through the coil so the rate of change of magnetic flux is zero.

Thank you very much renormalize and kuruman
 
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