A cycle wheel is rotated with a speed of 240 rpm in a plane normal to horizontal component of earth’s magnetic field of 0.36 G. Find the value of induced current between the rim and axle of the wheel given, there are 16 spokes, each 70 cm long. The resistance of each spoke is 2 Ω.

$1.76\times 10^{-3} A$

The correct answer is option (2) : $1.76\times 10^{-3} A$

Induced emf (z) $=\frac{\beta \omega l^2}{2}$

$=\frac{0.36\times 10^{-4}\times 2 \pi f \times (70 \times 10^{-2})^2}{2}$

$=\frac{36\times 10^{-6}\times 8 \pi \times 4900 \times 10^{-4}}{2}$

$=18\times 8\times 6.28 \times 49 \times 10^{-8}$

$R_{eff}=\frac{2}{16}=\frac{1}{8}$

$I=R_{eff}=\frac{18\times 8\times 6.28\times 49 \times 10^{-8}}{\frac{1}{8}}$

$≈1.76\times 10^{-3}A$