6a. A 0.66-m aluminum bar is held with its length parallel to the east-west direction and dropped from a bridge. Just before the bar hits the river below, its speed is 26 m/s, and the emf induced across its length is 5.0 x 10^-4 V. Assuming the horizontal component of the Earth's magnetic field at the location of the bar points directly north, (a) determine the magnitude of the horizontal component of the Earth's magnetic field, and (b) state whether the east end or the west end of the bar is positive.

a.

b.

6B. Two circuits contain an emf produced by a moving metal rod, like that shown in the drawing. The speed of the rod is the same in each circuit, but the bulb in circuit 1 has one-half the resistance of the bulb in circuit 2. The circuits are otherwise identical. The resistance of the light bulb in circuit 1 is 51 ?, and that in circuit 2 is 102 ?. Determine (a) the ratio ?₁/?₂ of the emfs and (b) the ratio I₁/I₂ of the currents in the circuits. (c) If the speed of the rod in circuit 1 were twice that in circuit 2, what would be the ratio P₁/P₂ of the powers in the circuits?