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

Explanation

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`
` therefore e = (-dphi)/(dt) = (-mu_0 )/(2pi) ia^2 (d)/(dt) (1/r) = (-mu_0)/(2pi) ia^2 = ((-1)/(r^2)) (dr)/(dt)`
Hence the induced emf in the loop is
`e = (mu_0)/(2pi) i (a^2)/(r^2) v ( because (dr)/(dt) = v)`