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The conductor `ABCDE` has the shape shown. It is lies in the `YZ` plane, with `A` and `E` on the `y`axis. When it moves with a velocity `v` in a magnetic field `B` , an emf `e` is induced between `A` and `E` . (Choose the incorrect option)
image
A. `e0` , if `v` is the `y`-direction and `B` is in the `x`-direction
B. `e=2Blambdav` , if `v` is in the `y`-direction and `B` is in the `x`-direction
C. `e=Blambdav` , if `v` in the z-direction and `B` is in the `x`-direction
D. `e=Blambdav` , if `v` is in the `x`-direction and `B` is in the `z`-direction

1 Answer

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Best answer
Correct Answer - B
`ABCDE` is equivalent to straight lentght `lambda`
(1) `e=0`
(3) `vec(v)=vhatk` , `vec(B)=Bhati` , `vec(l)=lambdahatj`
`e=Bvlambda`
(4) `vec(v)=vhati , hatl=lambdahatj , vec(B)=Bhatk`
`e=Bvlambda`
(3)
Magnetic field at distance `x` due to long wire
`B=(mu_(0)i)/(2pix),ox`
`de=Bvdx`
`e=(mu_(0)iv)/(2pi)int _(a)^(a+L)(dx)/(x)=(mu_(0)iv)/(2pi)|1nx|_(a)^(a+L)`
`=(mu_(0)iv)/(2pi)1n((a+L)/(a))`
`=(mu_(0)iv)/(2pi)1n(1+(L)/(a)) V_(A)-V_(B)=e`
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