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If I were rotating a disc of radius $r$ with an angular velocity $w$ completely enclosed by a uniform magnetic field $B$, perpendicular to the plane, will there be any emf produced? And how will the current flow?

I am aware that the motional emf produced is similar to that produced between two ends of a rod with length $r$ rotating around a circular conducting ring (radius $r$) with one end at the centre and the other touching the circumference of the ring. But how does the current flow? And the emf is between what two points?

The formula of the emf is $$\frac{wBR^{2}}{2}$$

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Yes, there will be current, but only for a short time at the beginning of the rotation. If the disc is metal, then it has free electrons. When you rotate the disc anti-clockwise, the perpendicular magnetic field (say upwards), due to Lorentz Force, will push the electrons towards the centre of the disc. This movement of electrons will create a current moving out of the centre. The electrons will get accumulated at the centre and the current will stop eventually.

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  • $\begingroup$ I am assuming that you did not connect the centre and the edge with a wire. Otherwise, there will be a continuous flow of current. $\endgroup$ Aug 3, 2021 at 15:49
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You are referring to the Homopolar Generator or else called Faraday disc Principle of operation.

Due the rotation of the disc and the Lorentz force the charges will move on the plane of rotation of the disc, spiralling inwards to the center of the disc uniformly through its thickness. It is a cylinder after all. This creates a steady (keeping rpm of the disc constant) emf voltage between the rim of the disc and its center (negative voltage pole) which can be then sampled by two pickup wires (brushes) touching its rim and center. A steady flow of current (d.c.) can be then redirected into an external electric circuit. The external circuit connected via the pickup wires to the disc acts like a shunt electrical load to the Faraday disc.

A further interesting question would be is there a constant electrical current present (not to be confused with Eddy currents) in a Faraday disc without a shunt?

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