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Physics
Classical Physics
Electromagnetism
Confusing diagram of a rotating coil in a magnetic field
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[QUOTE="vanhees71, post: 6861168, member: 260864"] Formulae are much more accurate than any picture and sometimes easier to understand. I guess what they mean to depict is that there is a (for simplicity homogeneous) magnetic field, ##\vec{B}=B \vec{e}_3##, and a rectangular coil with ##N## windings rotating around a perpendicular axis, say the 1-axis, i.e., it's ##\vec{\omega}=\omega \vec{e}_1##. Let's assume the loop is initially oriented such that the rectangle is in the 12-plane. Then the surface-normal vector is given by ##\vec{n}=(0,\sin(\omega t),\cos(\omega t)##. Unfortunately I cannot read the scanned book page well. I guess what they plot is the emf. So let's calculate the emf. from Faraday's Law. It's given by ##\mathcal{E}=-\dot{\Phi}##, where ##\Phi## is the flux of the magnetic field through the surface. Let ##a## and ##b## the lengths of the sides of the rectangular ##N##-fold loop. Then $$\Phi=N \vec{B} \cdot a b \vec{n} =a b N B \cos(\omega t) \; \Rightarrow \; \mathcal{E}=-\dot{\Phi}= a b B N \omega \sin(\omega t).$$ [/QUOTE]
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Physics
Classical Physics
Electromagnetism
Confusing diagram of a rotating coil in a magnetic field
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