A movable bar is pulled through a magnetic field with strength B = 0.2T along tw

Question

A movable bar is pulled through a magnetic field with strength B = 0.2T along two parallel rails. The field is into the page. The rails are a distance w = 4cm apart. At time t = 0 the bar is touching the rod connecting the two rails. The distance from the sliding rod to the fixed connecting bar as a function of time is given by l(t) = gamma t^4, where gamma is a constant. The velocity of the sliding rod is u(t) = dl/dt. (a) Compute the flux through the circuit formed by the bar, two rails, and the connecting rod as a function of time. Report the flux symbolically. (b) Compute the emf induced in the loop as a function of time. Report the emf symbolically. (c) At some point in the motion the sliding bar carries a current of 1.5A upward toward the top of the page. What is the magnetic force on the bar from the fixed magnetic field? Report both the magnitude and direction.

Explanation / Answer

(a) flux = B.A

= (0.2 ) ( l w) = 0.2 ( Y t^4) ( 0.04 m)

flux = 0.008 Y t^4

(B) Induced emf = d(flux) / dt

= 0.032 Y t^3

(C) F = I w B

= 1.5 x 0.04 x 0.2

= 0.012 N

F = Iw x B

F -> to the left

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