If the U-shaped conductor in the figure has resistivity ? , whereas that of the

Question

If the U-shaped conductor in the figure has resistivity ?, whereas that of the moving rod is negligible, derive a formula for the current I as a function of time.(Figure 1) Assume the rod starts at the bottom of the U at t=0, and moves with uniform speed v in the magnetic field B. The cross-sectional area of the rod and all parts of the U is A.

Express your answer in terms of the variables ?, v, B, A, t, and l.

If the U-shaped conductor in the figure has resistivity ?, whereas that of the moving rod is negligible, derive a formula for the current I as a function of time.(Figure 1) Assume the rod starts at the bottom of the U at t=0, and moves with uniform speed v in the magnetic field B. The cross-sectional area of the rod and all parts of the U is A. Express your answer in terms of the variables ?, v, B, A, t, and l. I(t)=

Explanation / Answer

Given thatthe magnitude of the magnetic field is B

         crossectionalarea of the each part is A

         speed ofrod is v

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    The indeced emf in the rod is ? =d?B/ dt

                                                  = BdA /dt

                                                   =B*L*v dt /dt

                                                   =BLv

where L is length of rod

Then then induced current is I = ? / R

But the resistance of the rod is R = ?L/A

Then induced current is I = [ BLv ] / ( ?L/A)

                                       = A*BLv/ ?L  

                                       =BAv / ?

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