Q158 / 180 · KCET 2016 · Physics
A wheel with \( 10 \) spokes each of length ' \( L \) ' \( m \) is rotated with a uniform angular velocity ' \( \omega \) ' in a
plane normal to the magnetic field 'B'. The emf induced between the axle and the rim of the
wheel.
plane normal to the magnetic field 'B'. The emf induced between the axle and the rim of the
wheel.
- A\( \frac{1}{2} N \omega B L^{2} \)
- Correct answerB\( \frac{1}{2} \omega B L^{2} \)
- C\( \omega B L^{2} \)
- D\( N \omega B L^{2} \)
Solution
Given, number of spokes \( =10 \); length of each spoke \( =L ; \) angular velocity \( =\omega \); angular field = B
Therefore, emf induced between axle and rim is given as
\( E=B l v_{\mathrm{avg}}=\frac{B l v}{2}=B L \frac{r \omega}{2} \)
Now, here \( r=L \)
\( \Rightarrow E=\frac{B L^{2} \omega}{2} \)
Thus, emf induced between the axle and rim of the wheel is \( \frac{1}{2} B L^{2} \omega \)
Therefore, emf induced between axle and rim is given as
\( E=B l v_{\mathrm{avg}}=\frac{B l v}{2}=B L \frac{r \omega}{2} \)
Now, here \( r=L \)
\( \Rightarrow E=\frac{B L^{2} \omega}{2} \)
Thus, emf induced between the axle and rim of the wheel is \( \frac{1}{2} B L^{2} \omega \)
Hence, the correct answer is option: 'B'.