This problem explores how a current-carrying wire can be accelerated by a magnet

Question

This problem explores how a current-carrying wire can be accelerated by a magnetic field. You will use the ideas of magnetic flux and the EMF due to change of flux through a loop. Note that there is an involved follow-up part that will be shown once you have found the answer to Part B.

A conducting rod is free to slide on two parallel rails with negligible friction. At the right end of the rails, a voltage source of strength V in series with a resistor of resistance R makes a closed circuit together with the rails and the rod. The rails and the rod are taken to be perfect conductors. The rails extend to infinity on the left. The arrangement is shown in the figure.

(Figure 1)

There is a uniform magnetic field of magnitude B, pervading all space, perpendicular to the plane of rod and rails. The rod is released from rest, and it is observed that it accelerates to the left. In what direction does the magnetic field point?

A conducting rod is free to slide on two parallel rails with negligible friction. At the right end of the rails, a voltage source of strength  in series with a resistor of resistance  makes a closed circuit together with the rails and the rod. The rails and the rod are taken to be perfect conductors. The rails extend to infinity on the left. The arrangement is shown in the figure.

A) There is a uniform magnetic field of magnitude , pervading all space, perpendicular to the plane of rod and rails. The rod is released from rest, and it is observed that it accelerates to the left. In what direction does the magnetic field point?

B) Assuming that the rails have no resistance, what is the most accurate qualitative description of the motion of the rod?

Explanation / Answer

1. From left hand rule : The field is pointed out of the page
2. Flux change = BLv
Reduced voltage = V - Blv
Reduced current = (V - Blv)/R
Reduced force = BIL = B(V - BLv)L/R
hence, its acc will reduce to a certian threshold velocity

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