hw8_p5405_f02 - incline with acceleration g sin θ However...

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HW 8 Phys5405 f02 11/19/02 1) Consider a long inclined plane, inclined with respect to the horizontal at an angle θ . Running along the full length of the incline are two parallel conducting rails of say, square cross section, spaced a distance d apart. At the top of the incline the rails are connected by a fixed similar rail of of length d. Further down the incline is a similar rail of length d and mass m, free to move along the incline without friction. This rail makes electrical connect with the two long rails as it moves so as to complete an electric circuit. Take the resistance of the circuit to be R. If there was no magnetic field, the free rail would move down the
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Unformatted text preview: incline with acceleration g sin θ . However, suppose there is a magnetic field in the vertical direction (y) where B =B cos ωt e y , where B ,ω are constant. Find an equation of motion for the free rail. You don’t have to solve this equation. For definiteness take x=0 at the top of the incline with positive x going down the incline. 2) Find the non relativistic hamiltonian for a spinless charged particle in a constant mag-netic field in the z direction. Choose your A so that the hamiltonian contains the angular momentum operator L z . 1...
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