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:

  • 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}} $



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