Electro Magnetic Induction And Alternating Currents Question 506
Question: A metallic rod of length T is tied to a string of length U and made to rotate with angular speed co on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ‘B’ in the region, the e.m.f. induced across the ends of the rod is
Options:
A) $ \frac{2B\omega {{\ell }^{2}}}{2} $
B) $ \frac{3B\omega {{\ell }^{2}}}{2} $
C) $ \frac{4B\omega {{\ell }^{2}}}{2} $
D) $ \frac{5B\omega {{\ell }^{2}}}{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
- Here, induced e.m.f. $ e=\int\limits_{2\ell }^{3\ell }{(\omega x)Bdx}=B\omega \frac{[{{(3\ell )}^{2}}-{{(2\ell )}^{2}}]}{2} $ $ =\frac{5B{{\ell }^{2}}\omega }{2} $
