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a rectangular loop, as shown in Fig. 3.6...

a rectangular loop, as shown in Fig. 3.66, moves away from an infinitely long wire carrying a current `I. Find the emf induced in the rectangualr loop.

Text Solution

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`E=B_(1)LV-B_(2)Lv=(mu_(0)i)/(2pix)Lv-(mu_(0)i)/(2pi(x+b))Lv=(mu_(0)iLbv)/(2pix(x+b))`

Alter:
Consider a small segment of width dy at a distance y from the wire.
Let flux through the segment be `dphi`.

`:. dphi=(mu_(0)i)/(2piy)Ldy " " :. phi=(mu_(0)iL)/(2pi) int_(x)^(x+b)(dy)/(y)=(mu_(0)iL)/(2pi)(l""n(x+b)-l""nx)`
Now `(dphi)/(dt)=(mu_(0)iL)/(2pi)[(1)/(x+b)(dx)/(dt)-(1)/(x)(dx)/(dt)]v=(-mu_(0)ibLv)/(2pix(x+b))`
`:.` induced emf `=(mu_(0)ibLv)/(2pix(x+b))`
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