Consider an infinitely long wire carrying a current I (t),
With `(dI)/(dt) = lambda` = constant . Find the current produced in the rectangular loop of wire ABCD if its resistance is R, Fig

Explanation

Let us consider a strip of length l and width dr at a distance r from infinite long current carrying wire. The magnetic field at strip due to current carrying wire is given by Field `B(r)=(mu_0I)/(2pir)` (out of paper)
Total flux through the loop is Flux `=(mu_0I)/(2pi)lint_(x_O)^x (dr)/(r)=(mu_oI)/(2pi)In(x)/(x_o)`......(i)
The emf induced canbe obtained by differentiating the eq. (i) wrt t and then applying Ohm's law
`(epsilon)/(R)=I`
We have, induced current `=(1)/(R)(dphi)/(dt)=(epsilon)/(R)=(mu_0I)/(2pi)(lambda)/(R)In(x)/(x_0)`
`(because(dI)/(dt)=lambda)`.