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?© BrainMass Inc. brainmass.com October 16, 2018, 9:15 pm ad1c9bdddf
Step by step solution provided.
Magnetic fields, Ampere's law, current
1. Two wires shown are separated by d=10 cm and carry currents of I=5.0 A in opposite directions. Find the magnitude and direction of the net magnetic field at:
i) A point midway between the wires.
ii) A point 2s=20 cm to the left of the wire on the left.
2. Using Ampere's law, erive the magnetic field produced at a point:
i) r inside a wire of radius R.
ii) r outside the wire of radius R.
3. A conducting bar of mass m, length l, makes a circuit with resistor R. The bar moves to the left without friction in a horizontal plane, moving on parallel conducting rails as shown in the figure below. A constant magnetic field B is directed perpendicular, in the outward direction, to the plane of the page.
a) At what constant speed should the bar move to priduce an 8.5 mA current in the resistor?
b) What is the direction of the current?
c) At what rate is energy delivered to the resistor?
d) Where is the energy coming that is delivered to the resistor?