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
Let us consider a small element at a distance from the centre of the rod rotating with angular velocity about its axis perpendicular bisector.
Formula used: The emf induced is given by
The emf is induced in the rod because of the small element is
Where is the emf induced in that small element
B is the magnetic field
is the angular velocity of the small element
is the length of the small element
The emf induced across the centre and the end of the rod is found by the integration of the above relation with respect to x from limit o to
The potential difference between the centre of the rod and an end is .
Thus, option B is correct.