A conducting bar of length l moves to the right on two frictionless rails, as sh

Question

A conducting bar of length l moves to the right on two frictionless rails, as shown in the figure below. A uniform magnetic field directed into the page has a magnitude of 2.80 T. Assume l = 32 cm and R = 8.9 Ohm. At what constant speed should the bar move to produce an 8.3 mA current in the resistor? m/s What is the direction of this induced current? At what rate is energy delivered to the resistor? mJ/s Explain the origin of the energy being delivered to the resistor. This answer has not been graded yet.

Explanation / Answer

(a) F V = IR and V = BLv   

put these together and you get

BLv = IR

v = IR / BL = 0.0083 * 8.9 / 2.8 * 0.32 = 0.0824 m/s direction will be counterclockwise (from bottom of bar to top of bar; or downward through the resistor).

(b) rate of energy = I^2 R = 0.0083^2 * 8.9 = 0.000613 J/s = 0.613 mJ/s

(c) the source of the energy is the work done by the applied force.

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