If the U-Shaped conductor in fig below has resisted ?, whereas that of the moving rod is negligible, derive a formula for the current I as a function of time. Assume that the rod has length l, 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.

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Aubree Mcintyre · Accepted Answer

If we assume that the movable rod stars at the bottom of the U, in a times t it will have moved a distance x=vt. For the resistance of the U; R=pLA=ρ(2vt+l)A.  The induced emf is;  θ=Blv  so the induced current is;  I=θR=Blvρ(2vt+l)A  =BlvAρ(2vt+l)

If the U-Shaped conductor in fig below has resisted

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