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As shown in the figure, a rectangular lo...

As shown in the figure, a rectangular loop of a conducting wire is moving away with a constant velocity v in a perpendicular direction from a very long straight conductor carrying a steady current I. When the breadth of the rectangular loop is very small compared to its distance from the straight conductor, how does the emf E induced in the loop vary with time t?

A

`Eprop(1)/(t^(2))`

B

`Eprop(1)/(t)`

C

`Eprop-ln(t)`

D

`Eprop(1)/(t^(3))`

Text Solution

Verified by Experts

The correct Answer is:
A
Electromotive force,
`E=-(dphi)/(dt)=-(d)/(dt)(vecB.vecA)`
`=-A(dB)/(dt)" "[because " the direction of B and A are same"]`
`=-A(d)/(dt)((mu_(0)I)/(2pivt))`
[Since for an infinitely long conductor, magnetic field at a distance r is, `B=(mu_(0)I)/(2pir)."Now, "r=vxxt`]
`=-(Amu_(0)I)/(2piv)(d)/(dt)(t^(-1))=(Amu_(0)I)/(2piv)t^(-2)`
`therefore Eprop(1)/(t^(2))`
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