A metal wire of mass m slides without friction on two horizontal rails spaced a

Question

A metal wire of mass m slides without friction on two horizontal rails spaced a distance d apart, as in the figure below. The track lies in a vertical uniform magnetic field B Bar. Generator G produces a constant current j in the wire and the rails (even as the wire moves). Find the velocity of the wire's motion as a function of time, assuming it to be stationary at t = 0. (Use the following as necessary: m, d, i, t, and B for the magnitude of B Bar, Enter the sign of the expression, taking right to be positive.) v Vector = Bidt/m In the figure below, a current j = 25 A is set up in a long hairpin conductor formed by bending a wire into a semicircle of radius R = 7.0 mm. Point b is midway between the straight sections and so distant from the semicircle that each straight section can be approximated as being an infinite wire, What is the magnitude of B Bar at a?.0184 T What is the direction of B Vector at a? into the page out of the page What is the magnitude of B Bar at b?.0143 T What is the direction of B Bar at b? into the page out of the page

Explanation / Answer

(1) The current i in the wire (from the source G) is sitting in the magnetic field B,
resulting in force towards the left. The wire is accelerating towards the left. As the
wire starts to move left, a current is induced in the opposite direction and the
induced current is proportional to the velocity, which is increasing. Finally, two
forces are at equilibrium, and the acceleration is zero. The velocity reaches
maximum value, i.e. terminal velocity.
FB=idB
Find=i’dB
i'=e/R=Bdv/R
FB=Find
v=iR/dB

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