As shown in Figure P6.6, a rod in a uniform magnetic field is free to slide on t

Question

As shown in Figure P6.6, a rod in a uniform magnetic field is free to slide on two rails. The resistances of the rod and the rails are negligible. Electrical continuity between the rails and the rod is assumed, so a current can flow through the rod. A damping force, Fj, tending to slow down the rod, is proportional to the square of the rod's speed as follows: Fd = kfu2 where kf = 1500. Assume that the inductance in this circuit can be ignored. Find the steady state speed u of the rod, assuming the system extends endlessly to the right.

Explanation / Answer

F= ilB= Fd

i = 50/0.1 = 500A

500*2*1 = 1500 *u2

therefore u = (2/3)1/2 = 0.8164(m/sec)

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