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```Name:_____________________________________________________ Section: A B Quiz 05A: Motional EMF A metal bar is made to slide horizontally, on top of two very thin, parallel L"
B (out)
metal rails, at a speed v=5m/s, through a uniform magnetic field, B, with the B-­‐vector pointing vertically out of the plane of the drawing, as shown in the figure to the left. A capacitor of unknown capacitance, C, is Sliding'Metal'Bar'
connected to the two metal rails with metal wires. Assume in the following that the resistances of the bar, the rails, the contacts between v
bar and rails, and of all connecting wires are negligibly small. Also neglect friction between the bar and the rails. As the bar is set into motion, an electric charge of Q=12μC builds up on one of the capacitor plates, with an opposite charge, of −12μC, building up on the other, opposing plate. After that charge build-­‐up, no more current flows in the rails, the bar or the wires, as the bar keeps moving. Assume a magnetic field strength of B ≡|B|=2T and a spacing of L=0.3m C"
between the two rails. __________________________________________________________________________________________ (a) Find the strength of the electric field, E ≡ |E|, that builds up inside the metal bar, as the bar is set into motion. [Hint: Consider the magnetic force, Fm, acting on any charge carrier inside the sliding bar, due to B. In the absence of current flow inside the bar, that force, Fm, must be exactly canceled by the electric force Fe, acting on the charge carrier, due to E. Also: the carrier’s charge, q, drops out!] E =___________V/m __________________________________________________________________________________________ (b) In Part (a), find the direction of that electric field vector, E, inside the bar. Does E point: (A) out of the drawing, (B) into the drawing, (C) to the left , (D) to the right, (E) towards the top of the drawing, or (F) towards the bottom of the drawing ? __________________________________________________________________________________________ (c) Find the capacitance C, stated in units of μF. [Hint: The voltage drop between the two capacitor plates is Vc = Q/C. How is Vc related to the voltage drop Vb along the sliding metal bar ? How is Vb related to E ?] C=____________ μF __________________________________________________________________________________________ (d) Which one of the two capacitor plates builds up the positive charge, Q, if the bar is made to slide towards the capacitor, as shown in the figure above ? (A) the left plate (B) the right plate Which one of the two capacitor plates builds up the positive charge, Q, if the bar’s direction of motion is reversed, i.e., the bar is made to slide away from the capacitor? (A) the left plate (B) the right plate __________________________________________________________________________________________ (e) If the capacitor in the circuit above is replaced by a 10Ω resistor a current, I, will flow through the resistor, the connecting wires, the rails and the sliding bar. Assuming the bar is kept moving at the same, constant speed, v=5m/s, what is the rate of heat generation (the Joule heating power) in that resistor? [Hint: The voltage drop Vb along the sliding metal bar remains the same as before, since the bar’s, rails’ and connection wires’ resistances are negligible.] P=____________ W __________________________________________________________________________________________ (f) In Part (e), a constant external “pulling” force, Fext, must be applied to the bar in order to keep it moving at constant speed. Find the magnitude of that force, Fext ≡ |Fext|. [Hint: Use either this: Fext must do work on the bar at the same rate as heat is generated in the resistor. Or this: To keep the speed v constant, the magnetic force on the current-­‐carrying bar, FB, cancels Fext .] Fext=___________N __________________________________________________________________________________________ ```
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