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Two metallic rings of radius R are rolling on a metallic rod. A magnetic field of magnitude B is applied in the region. The magnitude of potential difference between points A and C on the two rings (as shown), will be

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$8 B ω R^{2}$

$0$

$4 B ω R^{2}$

$2 B ω R^{2}$

answer is B.

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Detailed Solution

$V_{A} - V_{0} = \frac{B ω {(2 R)}^{2}}{2} = 2 B ω R^{2} ......... (i) V_{0} - V_{C} = \frac{B ω {(2 R)}^{2}}{2} = 2 B ω R^{2} ......... (i i)$

Adding these two equations, we get

$V_{A} - V_{C} = 4 B ω R^{2}$

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