If the U-shaped conductor in the figure has resistivity 1.68 x 10 -8 %u03A9.m, w

Question

If the U-shaped conductor in the figure has resistivity 1.68 x 10-8 %u03A9.m, whereas that of the moving rod is negligible, find the current I at time t = 2.85 s. Assume the rod has length L = 10.8 cm, starts at the bottom of the U at t = 0, and moves with uniform speed v = 3.43 m/s in the constant magnetic field B = 0.00369 T shown in the figure. The cross-sectional area of the rod and all parts of the U is 3.37 x 10-6 m2.
I =

HINT: What is the rate of change of flux through the loop? What emf is induced?

Please include solution as well as answer.

Explanation / Answer

Given thatthe magnitude of the magnetic field is B          crossectionalarea of the each part is A          speed ofrod is v -----------------------------------------------------------------------     The indeced emf in the rod is %u03B5 =d%u03C6B/ dt                                                   = BdA /dt                                                    =B*L*v dt /dt                                                    =BLv where L is length of rod Then then induced current is I = %u03B5 / R But the resistance of the rod is R = %u03C1L/A Then induced current is I = [ BLv ] / ( %u03C1L/A)                                        = A*BLv/ %u03C1L                                          =BAv / %u03C1                    

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