For a coil rotating in a uniform magnetic field, the phase difference between the magnetic flux linked with the coil and the current induced in it is
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If
\[
\Phi=\Phi_0\cos\omega t,
\]
then
\[
\boxed{
e=-\frac{d\Phi}{dt}\propto\sin\omega t
}
\]
Hence, the induced current leads the magnetic flux by
\[
\boxed{90^\circ.}
\]