Electro Magnetic Induction And Alternating Currents Question 471
Question: A wooden stick of length $ 3\ell $ is rotated about an end with constant angular velocity $ \omega $ in a uniform magnetic field B perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the potential difference across the whole length of the stick is
Options:
A) $ \frac{9B\omega {{\ell }^{2}}}{2} $
B) $ \frac{4B\omega {{\ell }^{2}}}{2} $
C) $ \frac{5B\omega {{\ell }^{2}}}{2} $
D) $ \frac{B\omega {{\ell }^{2}}}{2} $
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Answer:
Correct Answer: C
Solution:
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For $ A:e_{A}=\frac{1}{2}B\omega {{(3\ell )}^{2}} $
and $ e_{B}=\frac{1}{2}B(-\omega ){{(2\ell )}^{2}} $
Resultant induced emf will be $ e=e_{A}+e_{B}=\frac{1}{2}B\omega {{\ell }^{2}}(9-4) $
or $ e=\frac{5}{2}B\omega {{\ell }^{2}} $
