Introduction Motional EMF: Moving Rods
A long wire with resistance per unit length 2 Ω/m is bent into a long rectangular frame of width 3 m that is open at one end. The frame is fixed to a horizontal table top with the two long sides acting as frictionless rails. A perfectly conducting rod moves on the rails with a constant velocity of 3 m/s in a direction parallel to the rails, from the closed end of the rectangular frame towards the open end. The length of the moving rod is 10 m and the rod is placed perpendicular to the rails, symmetrically between the two rails. There is a uniform vertical magnetic field of B = 1.4 x 10-3 T everywhere in space. At t = 0 s, the rod is at a distance of 2 m from the closed end of the rails. Find the emf across the two end points of the rod.
A 12 Ω resistor and a 24 Ω resistor are connected by perfectly conducting parallel rails as shown. The distance between the two rails is 3 m. A rod with 4 Ω resistance is placed perpendicular to the rails (with its ends on the two rails). The rod moves with a velocity of 5 m/s parallel to the rails from the 12 Ω resistor perpendicular to the plane of the system (pointing out of the diagram) as shown. Find the current i in towards 24 Ω resistor as shown. The whole system is immersed in a magnetic field B = 0.3 T perpendicular to the plane of the system (pointing out of the diagram) as shown. Find the current i in the 12 Ω in the direction it is marked on the diagram (with the proper sign).