An electromagnetic eddy-current brake - a simple example of the principle on which is based the regenerative brakes in hybrid cars and electric trains -- consists of a disk of conductivity o and thickness Az rotating about an axis through its center with a magnetic field B applied perpendicular to the plane of the disk over a small area a (see the diagram at right). Assuming the area a' to lie at a distance r from the axis, find an approximate expression for the torque tending to slow down the disk at the instant its angular velocity equals w. Think of the area segment as having length (= a in the radial direction , width w=a in the direction and thickness = Az in the z direction (B field is in the direction). Az