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Q.

Two identical conducting rings A and B of radius $R$ are rolling over a horizontal conducting plane with same speed $v$ but in opposite direction. A constant magnetic field $B$ is present pointing into the plane of paper. Then the potential difference between the highest points of the two rings is $x B v R$ then find $x$ .

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Detailed Solution

$V_{2} - V_{1} = \frac{1}{2} B ω {(2 R)}^{2} = 2 B R (ω R) = 2 B R v$

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$V_{3} - V_{4} = 2 B R v b u t V_{1} = V_{3}; \Rightarrow V_{2} - V_{4} = 4 B R v$

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Two identical conducting rings A and B of radius R are rolling over a horizontal conducting plane with same speed v but in opposite direction. A constant magnetic field B is present pointing into the plane of paper. Then the potential difference between the highest points of the two rings is xBvR then find x.