Engineering
Physics
Magnetic Flux and Faraday Law and Lenz Law
Question

A rigid wire loop of square shape having side of length L and resistance R is moving along the x-axis with a constant velocity v0 in the plane of the paper. At t = 0, the right edge of the loop enters a region of length 3L where there is a uniform magnetic field Bo into the plane of the paper, as shown in the figure. For sufficiently large v0, the loop eventually crosses the region. Let x be the location of the right edge of the loop. Let v(x), I(x) and F(x) represent the velocity of the loop, current in the loop, and force on the loop, respectively, as a function of x:. Counter-clockwise current is taken as positive.

Which of the following schematic plot(s) is(are) correct? (Ignore gravity)

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Solution

 i=BℓuR

 F=iℓB=−B2ℓ2uR

 mudvdx=−B2ℓ2vR

 −∫v0vv dx=B2ℓ2mR u∫0xdx

 v0– v =B2ℓ2mRx

 v = v0–B2ℓ2mRx

 i=BℓvR=BℓRv0−B3ℓ3mR2x

 F=−B2ℓ2R  (v0−B2ℓ2mRx)