A current `i_(0)` is flowing in a long straigh wire situation near a rectangular loop as shown. If the current in the loop as shown . If the current decays iniformly to zero in time `t_(0)` find the emf include in the circuit and determine direction of induced current in the loop .

Explanation

Consider a strip of rectangular of width `dx` at a distance `x` from the wire.
The magnetic field at the location of strip
`B=(mu_(0)i)/(2pix),ox`
Flux through strip
`dphi=(BdA)=(mu_(0)i)/(2pix)adx`
Total flux `phi=(mu_(0)ia)/(2pi)int_(d)^(2d)(dx)/(x)=(mu_(0)ia)/(2pi)|1nx|_(d)^(2d)`
`=(mu_(0)ia)/(2pi)[In(2d)-In(d)]`
`=(mu_(0)ia)/(2pi)1n((2d)/(d))=(mu_(0)ia1n2)/(2pi)`
`t=0` , `phi_(1)=(mu_(0)i_(0)a1n2)/(2pi)`
`t=t_(0),phi_(2)=0`
`|bar(e)|=(Deltaphi)/(Deltat)=(mu_(0)i_(0)a1n2)/(2pit_(0))`
Flux is decreases, induced current will be anticlockwise.