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.

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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`

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