The long straight wire in figure (a) carries a constant current `i`. A metal bar of length `i` is moving at constant velocity `v` as shown in figure. Point a is a distance d from the wire.

(a) Calculate the emf induced in the bar.
(b) Which point `a` or `b` is at higher potential?
(c) If the bar is replaced by a rectangular wire loop of resistance `R`, what is the magnitude of current induced in the loop?

Explanation

a. At a distance `dx` from the wire, magnetic field over the wire ab is
`B=mu_0/(2pi) i/x`
`dV=Bvdx=((mu_0i)/(2pix))vdx`
`:.` Total emf `=int_(x=d)^(x=d+l) dV`
b. Magnetic field due to current `i` over the wire `ab` is inwards. Velolcity of wire `ab` is towards right. Applying right hand rule, we can see that a point is at higher potential.
c. Net change in flux through the loop abcd is zero. Hence, induced emf is zero. So, induced current is zero.