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Find the current in the wire for the con...

Find the current in the wire for the configuration shown in figure. Wire PQ has negligible resistance. `vecB`, the magnetic field is coming out of the paper. `theta` is a fixed angle made by PQ travelling smoothly over two conducting parallel wires separated by a distance d.

Text Solution

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Induce emf in rod can be given by ,
`epsilon=Bvl`
Here, `vecB, vecv` and `vecl` all should be mutually perpendicular and if it is not then we consider their perpendicular component.

Here `vecB` and `vecv` is perpendicular to each other but length of rod PQ is not perpendicular to `vecv` and `vecB`. But Isine component is perpendicular to both `vecv` and `vecB`.
From figure , lsin`theta`=perpendicular distance between two wire (d)
`therefore lsintheta =d`
`therefore epsilon=Bvd`
Induced emf `epsilon=Bv(lsin theta) = Bvd`
Induced current `I=epsilon IR`
`=(Bvd)/R`
Direction of this induced current is in clockwise direction according to Lenz.s law.
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