Question

A rod of length l rotates with a 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 two ends of the rod is
(a) zero
(b) 12Blω2
(c) Blω2
(d) 2Blω2.

Answer 1

Potential Difference is ZERO (Option A)

Explanation:

Lets take an element dx which is x distance from the center of a rod rotating with some angular velocity about its perpendicular bisector.

Now the emf being induced in element of rod due to its motion is

$de = B\omega xdx$

EMF being induced between rods center and one of its own end is

$\int de = \int_{0}^{l}B\omega xdx$

⇒ $e = B\omega (\frac{x^2}{2}) ^{\frac{l}{2}}_0$

⇒ $e = \frac {1}{8}B\omega l^2$

The emf at both ends is same.

Hence, Potential Difference in-between two ends 0 (ZERO)