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# Force on a current carrying cross bar in a magnetic field

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A schematic 'rail gun motor' is shown in figure 1 (see attachment). Two horizontal parallel rails are a distance L apart and are joined at one end by a voltage source producing a fixed voltage Vo. A crossbar of mass m completes the circuit. The cross bar is free to slide on the rails, always remaining perpendicular to them. All frictional forces are negligible. The resistance of the circuit made by the rails, the voltage source and the crossbar can be taken to have constant value, R. A constant uniform magnetic field B acts into the page throughout the whole region.

a) The cross bar is initially held in fixed position, and is then suddenly released. Using the magnetic force law for a current element, obtain an expression for the instantaneous magnitude of the acceleration of the crossbar immediately after it has been released. With the magnetic field and voltage source shown in the figure, does the crossbar move to the left or right? Explain your answer.

b) Show that the crossbar approaches a steady speed of v = Vo /(BL). What is the current flowing through the circuit when this speed is reached?