Problem 2
A conducting bar of length L and mass m slides without friction on vertical rails separated by L in a uniform magnetic field B perpendicular to their plane. The rails are connected through resistance R; neglect other resistance. Released from rest, find terminal speed and Joule power at that speed. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.
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The moving bar cuts magnetic field lines, giving emf B L v; Ohm's law gives the current. This follows from the chosen physical model and the stated initial conditions; the sign convention must remain consistent throughout. A dimensional check catches algebraic errors before the result is interpreted.