Question

A wheel with 20 metallic spokes each of length 0.8 m long is rotated with a speed of 120 revolution per minute in a plane normal to the horizontal component of earth magnetic field H at a place. If H = 0.4 x 10-4 T at the place, then induced emf between the axle and the rim of the wheel is

• A. 2.3 × 10-4 V
• B. 3.1 × l0-4V
• C. 2.9 × 10-4 V
• D. 1.61 × 10-4 V

Answer 1

Answer: (D)

1.61 × 10-4 V

Answer 2

Here , $H = B = 0.4 \times 10^{- 4}T,l = 0.8m$

$\upsilon = 120rpm = 2rps$

Emf induced across the ends of each spoke

$\varepsilon = \frac{1}{2}B\omega l^{2}$

$= \frac{1}{2}B(2\pi\upsilon)l^{2}$ $(\because\omega = 2\pi\upsilon)$

$= B\pi\upsilon l^{2}$

$\therefore\varepsilon = 0.4 \times 10^{- 4} \times \pi \times 2 \times (0.8)^{2}$

$= 1.61 \times 10^{- 4}V$

Note : Number of spokes is not relevant because the emfs across the spoke area is parallel.