Question

Derive an expression for the total emf induced in a conducting rotating rod.

Answer 1

Consider a conducting rod rotating around a pivot at one end in a uniform magnetic field that is perpendicular to the plane of rotation.

Now consider a small element dr of the rod at a distance r from the pivot moving with velocity `barv` in magnetic field `barB` and has an induced emf generated in it like a sliding rod.

The induced emf de in the small segment dr of the rotating conductor.

`de = Bvdr` 

Total induced emf in rotating rod

`e =intde = intBvdr`

`e=intBomegardr=Bomegaint_0^lrdr`

`=Bomegal^2/2`

`e=1/2Bomegal^2`