6.6 M OTIONAL E LECTROMOTIVE F ORCE

. M OTIONAL E LECTROMOTIVE F ORCE Let us consider a straight conductor moving in a uniform and time- independent magnetic field. Figure . shows a rectangular conductor PQRS in which the conductor PQ is free to move. The rod PQ is moved towards the left with a constant velocity v as shown in the figure. Assume that there is no loss of energy due to friction. PQRS forms a closed circuit enclosing an area that changes as PQ moves. It is placed in a uniform magnetic field B which is perpendicular to the plane of this system. If the length RQ = x and RS = l , the magnetic flux Φ B enclosed by the loop PQRS will be Φ B = Blx Since x is changing with time, the rate of change of flux Φ B will induce an emf given by: ( – d – B Blx Φ ε = – x Bl Blv t = ( . ) FIGURE . The arm PQ is moved to the left side, thus decreasing the area of the rectangular loop. This movement induces a current I as shown.