# Currents induced by rotation of a coil about magnetic field lines If the coil on the left is rotated about the magnetic field lines, will there be an induced current? I know that the flux concerns only the component of the magnetic field perpendicular to the plane of the coil, so even if it is rotated, I assume the perpendicular component will remain the same. Just want to confirm this. Thanks

The flux is defined as integal {if you don't know calculus, take this as a sum} of $$\int_\Gamma \vec B \dot \, \mathrm d \vec A$$ where dA points out the surface $$\Gamma$$.
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If coil has length $L$, rotating at angular speed $\omega$, and the induction circuit is at a distance $s$ from the coil, then our approximations: The extreme part of the coil must have speed lower than speed of light: $L\omega\ll c$. And the time for the magnetic field arrive the circuit must be close to zero: $\Delta t = s/c\ll 1$. If this is true, you can calculate the emf with induction law approximating that the magnetic field rotates nicely with the coil: $$\mbox{emf} = -\frac{d\Phi}{dt}$$