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A rectangular loop of sides 8 cm and 2 c...

A rectangular loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform megnetic field of magnitude 0.3 tesla directed normal to the loop. What is the voltage developed acorss the cut if velocity of the loop is `1 cm s^(-1)` in a direction normal to the (i) longer side (ii) shorter side of the loop ? For how long does the induced voltage last in each case?

Text Solution

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Given, magnetic field, B = 0.3 T
Length of longer side, `l = 8 cm = 8 xx 10^(-2) m`
Length of shorter side, `b= 2 cm = 2 xx 10^(-2) m`
`v = "1 cm" s^(-1) 10^(-2) m s^(-1)`
(a) When velocity is normal to longer side, emf developed across the cut will be
`epsilon = Blv`
`epsilon=0.3 xx 8 xx 10^(-2) xx 10^(-2)=2.4 xx 10^(-4)V`
Time taken to come out of magnetic field
`=(2 xx 10^(-2))/(10^(-2))=2 s`
(b) When velocity is normal to shorter side, emf developed across the cut will be
`epsilon = Bbv`
`epsilon=0.3 xx 2 xx 10^(-2) xx 10^(-2)=0.6 xx 10^(-4)V`
Time taken to come out of magnetic field
`=(8 xx 10^(-2))/(10^(-2))=8 s`
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