Question

Figure shows a rectangular conductor PQRS in which the Conductor PQ is free to move in a uniform magnetic field B perpendicular to the plane of the paper. The filed extends from x=0 to x=b and is zero for $x>b$. Assume that only the arm PQ possesses resistance r. when the arm PQ is pulled outward from x=0 to x=2b and is then moved back to x=0 with constant speed v, Determine the expression for the flux and induced emf. Sketch the variations of these quantities with distance $0\le x\le 2b$.

Answer 1

Let us consider forward motion from $x=0$ to $x=2b$, the flux ${\varphi }_B$ linked with the circuit SQPR is

${\varphi }_B=Blx$ $0<x<b$

$=Blb$ $b<x<2b$

The induced emf is

$E=\frac{-d\varphi }{dt}$

$\therefore E=BlV$ $0<x<b$

$=0$ $b<x<2b$