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At a certain instant in AC generator, when the normal of the plane (rectangular coil) makes an angle of 270 degrees with with the magnetic induction B, the value of emf is:

$E = -NAB\omega$

My teachers would usually say that this is the minimum value of emf that a generator produces. Does it really mean that? Or does the negative sign only mean that emf is at its peak value but the current is flowing in opposite direction?

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Yes. That's why it's named as alternating current. Briefing...

The magnetic flux linked to the coil is $\phi=NBA\ cos(\omega t)$ and the emf induced (according to Lenz' correction of Faraday's law, $$e=-NBA\frac{d(cos(\omega t))}{dt}=NBA\omega\ sin(\omega t)$$

Here, $NBA\omega$ is a constant which can be replaced by $E_0$ which is the maximum value of emf induced along the coil. When $\omega t=3\pi/2$ (i.e) when the normal makes the 270-degree angle, $e=-E_0$ which is the maximum negative voltage (or) simply the flow of current in the opposite direction. Please have an overview on the Wiki article...

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