As shown in the figure, a straight wire carries a steady current I. A metal bar is in contact with a pair of rails and is in upward motion with velocity of magnitude ν. The polarity of the induced emf in terminals X and Y is
A) X and Y are at the same potential.
B) X is positive and Y is negative.
C) Y is positive and X is negative.

Question

As shown in the figure, a straight wire carries a steady current I. A metal bar is in contact with a pair of rails and is in upward motion with velocity of magnitude ν. The polarity of the induced emf in terminals X and Y is 
A) X and Y are at the same potential. 
B) X is positive and Y is negative. 
C) Y is positive and X is negative.

Quizplus · Accepted Answer

According to Faraday's law of electromagnetic induction, a changing magnetic field induces an emf in a conductor. In this case, the metal bar is moving through the magnetic field created by the current-carrying wire, and thus a current is induced in the metal bar. By Lenz's law, the induced current will flow in a direction that opposes the change in magnetic flux through the loop formed by the metal bar and the rails.

In this case, since the metal bar is moving upward, the induced magnetic field inside the loop will be in the downward direction, and so the induced current will flow clockwise around the loop. Applying the right-hand rule to the loop, we can see that the induced current will create a magnetic field that opposes the field created by the current-carrying wire.

Using the right-hand rule for magnetic fields, we can see that the induced magnetic field in the loop will create a force that pushes the mobile electrons in the metal bar to the left, causing an accumulation of electrons at terminal X and a shortage of electrons at terminal Y. Thus, terminal X will be at a lower potential than terminal Y, and the polarity of the induced emf will be such that Y is positive and X is negative.

As Shown in the Figure, a Straight Wire Carries a Steady