A metal rod length l rotates about on end with a uniform angular velocity `omega`. A uniform magnetic field `vecB` exists in the direction of the axis of rotation. Calculate the emf induced between the ends of the rod. Neglect the centripetal force acting on the free electrons as they moving in circular paths.

Explanation

Consider an element dx of the rod at a distance x from the axis of rotation
The linear speed of this element is `omegax`
The element moves in a direction perpendicular to its length as well as perpendicular to the magnetic field
The emf induced between the ends of this element is `d epsilon = B omega x dx`
The emfs of all such elements will add to give the net emf between the ends of the rod
This emf is, therefore, ` epsilon = int d epsilon = int_0 ^l b omegax dx = (1(/(2) Bomegal^2`.