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Magnetic Forces and Torques

The 10-turn loop of wire shown in the figure below lies in a horizontal plane, parallel to a uniform horizontal magnetic field, and carries a 2.0 A current. The loop is free to rotate about a nonmagnetic axle through the center. A 50 g mass hangs from one edge of the loop. What magnetic field strength will prevent the loop from rotating about the axle?

Induction

You’ve decided to make the magnetic projectile launcher shown in the figure for your science project. An aluminum bar of length l slides along metal rails through a magnetic field B. The switch closes at t=0 s, while the bar is at rest, and a battery of emf E_{bat} starts a current flowing around the loop. The battery has internal resistance r. The resistances of the rails and the bar are effectively zero.

a) show that the bar reaches a terminal speed.

b) calculate that speed assuming that \mathcal{E}_{batt} = 1 \; V , r=0.1 \; \Omega , l=6 \; cm and B =0.5 \; T