Question

A rod of length 60 cm rotates with a uniform angular velocity $20 \, \text{rad} \, \text{s}^{-1}$ about its perpendicular bisector, in a uniform magnetic field $0.5 \, \text{T}$. The direction of the magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _____ V.

Answer 1

The given data:
Length of rod, $\ell = 60 \, \text{cm} = 0.6 \, \text{m}$, Angular velocity, $\omega = 20 \, \text{rad/s}$, Magnetic field, $B = 0.5 \, \text{T}$.

**The potential difference $V_O - V_A$ between the ends of a rod rotating in a magnetic field is given by: **
$V_O - V_A = \frac{B \omega \ell^2}{2}.$
**Substitute the values: **
$V_O - V_A = \frac{0.5 \times 20 \times (0.6)^2}{2} = \frac{0.5 \times 20 \times 0.36}{2}.$
$V_O - V_A = \frac{3.6}{2} = 1.8 \, \text{V}.$
However, since the magnetic field is parallel to the axis of rotation, no emf is induced across the rod. Therefore,
$V_A = V_B \implies V_A - V_B = 0.$
Answer: $0 \, \text{V}$