A metal disk of radius r rotates with an angular velocity omega about a vertical axis, through a uniform field B , pointing parallel to the axis of rotation. A circuit is made by connecting one end of a resistor with resistance R to the metal axle of the disk and the other end to a sliding contact, which touches the outer edge of the disk. Find the current I in the resistor.

The speed of a point on the disk at a distance r' for 0lt= r' lt=r from the axis is v=omega r' , so the force per unit charge is f_(mag)=v xx B=omega r' B radially outward. The emf is therefore,
epsilon=int f_(mag) * dl=int_0^r omega r' B dr'=1/2 omega Br^2
The current is then
I=epsilon/R=(omega Br^2)/R
https://en.wikipedia.org/wiki/Electromotive_force