Electro Magnetic Induction And Alternating Currents Question 510

Question: A conducting ring of radius r with a conducting spoke OA is in pure rolling on a horizontal surface in a region having a uniform magnetic field B as shown, v being the velocity of the centre of the ring. Then the potential difference $ V_{0}-V_{A} $ is:

Options:

A) $ \frac{Bvr}{2} $

B) $ \frac{3Bvr}{2} $

C) $ \frac{Bvr}{2} $

D) $ \frac{-3Bvr}{2} $

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Answer:

Correct Answer: C

Solution:

  • Considering pure rolling of OA about A: the induced emf across OA will be:
    $ | . {\vec{e}} | .=\frac{B\omega {{(r)}^{2}}}{2} $
    From lenz law, 0 will be the negative end, while A will be the positive end. Hence $ V_{0}-V_{A}=-\frac{B\omega r^{2}}{2} $


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