Question

A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

• A. $2.51 \times 10^{-4}\,V$
• B. $2.51 \times 10^{-5}\, V$
• C. $4.0\times 10^{-5}\, V$
• D. $2.51 \,V$

Answer 1

Answer: (A)

$2.51 \times 10^{-4}\,V$

Answer 2

$\varepsilon=\frac{1}{2} B \omega r^{2}$ $\varepsilon=\frac{1}{2}\times\left(0.4\times10^{-4}\right)\times\left(2\pi\left[\frac{120}{60}\right]\right)\left(1\right)^{2}$ $\varepsilon=0.8\pi\times10^{-4}$ $\varepsilon=2.512\times10^{-4}$ Volt