Electromagnetic Induction and Alternating Current 2 Question 1
2. A metallic rod of length $l$ is tied to a string of length $2 l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region, the emf induced across the ends of the rod is
(2013 Main)
(a) $\frac{2 B \omega l^{3}}{2}$
(b) $\frac{3 B \omega l^{3}}{2}$
(c) $\frac{4 B \omega l^{2}}{2}$
(d) $\frac{5 B \omega l^{2}}{2}$
Show Answer
Answer:
Correct Answer: 2. (d)
Solution:
- $e=\int _{2 l}^{3 l}(\omega x) B d x=B \omega \frac{\left[(3 l)^{2}-(2 l)^{2}\right]}{2}$
$$ =\frac{5 B l^{2} \omega}{2} $$
