Question

A rod of length l rotates with a small but uniform angular velocity ω about its perpendicular bisector. A uniform magnetic field B exists parallel to the axis of rotation. The potential difference between the centre of the rod and an end is ______________ .

Options

• Zero

• `1/8omegaBl^2`

• `1/2omegaBl^2`

• Bωl²

Answer 1

`1/8omegaBl^2`

 

Let us consider a small element dx at a distance x from the centre of the rod rotating with angular velocity ω about its perpendicular bisector. The emf induced in the rod because of this small element is given by

`de=Bvl=Bomegaxdx`

The emf induced across the centre and end of the rod is given by

`intde=int_0^(l/2)Bomegaxdx`

`rArrE=Bomega[x^2/x]_0^(l/2)`

`rArrE=1/8Bomegal^2`