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A square loop of side a is placed in the...

A square loop of side a is placed in the same plane as a long straight wire carrying a current i. The centre of the loop is at a distance r from the wire where r > > a. The loop is moved away from the wire with a constant velocity v. The induced e.m.f. in the loop is

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Magnetic field by the straight wire of current i at a distance r is
`B=(mu_(0)i)/(2pi r)`
flux associated with the loop is `phi = BA = (mu_(0)i)/(2pi r)a^(2)`
`:. e= (-d phi)/(dt)=(-mu_(0))/(2pi)ia^(2)(d)/(dt)((1)/(r))(dr)/(dt)`
Hence the induced emf in the loop is .
`e=(mu_(0))/(2pi)i(a^(2))/(r^(2))v` `( :. (dr)/(dt)=v)`
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