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A vertical ri...

Question

A vertical ring of radius $r$ and resistance $R$ falls vertically. It is in contact with two vertical rails which are joined at the top. The rails are without friction and resistance. There is a horizontal uniform magnetic field of magnitude $B$ perpendicular to the plane of the ring and the rails. When the speed of the ring is $v$ , the current in the top horizontal of the rail section is

0

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\frac{2 B r v}{R}

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\frac{4 B r v}{R}

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\frac{8 B r v}{R}

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Solution

The correct option is D $\frac{8 B r v}{R}$
$U p p e r p a r t o f t h e r r i n g h a s r e s i s t a n c e R / 2 a n d l o w e r p a r t h a s r e s i s t a n c e R / 2 a n d t h e y a r e c o n n e c t e d i n p a r a l l e l, t h u s, e f f e c t i v e r e s i s t a n c e = R / 4 i = \frac{E M F}{R e s i s t a n c e} = \frac{B v (2 r)}{R / 4} = \frac{8 B v r}{R}$

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