The long straight wire in the figure carries a current I that is decreasing with time at a constant rate.The circular loops A,B,and C all lie in a plane containing the wire.The induced emf in each of the loops A,B,and C is such that
A)no emf is induced in any of the loops.
B)a counterclockwise emf is induced in all the loops.
C)loop A has a clockwise emf,loop B has no induced emf,and loop C has a counterclockwise emf.
D)loop A has a counter-clockwise emf,loop B has no induced emf,and loop C has a clockwise emf.
E)loop A has a counter-clockwise emf,loops B and C have clockwise emfs.

Question

The long straight wire in the figure carries a current I that is decreasing with time at a constant rate.The circular loops A,B,and C all lie in a plane containing the wire.The induced emf in each of the loops A,B,and C is such that 
A)no emf is induced in any of the loops. 
B)a counterclockwise emf is induced in all the loops. 
C)loop A has a clockwise emf,loop B has no induced emf,and loop C has a counterclockwise emf. 
D)loop A has a counter-clockwise emf,loop B has no induced emf,and loop C has a clockwise emf. 
E)loop A has a counter-clockwise emf,loops B and C have clockwise emfs.

Quizplus · Accepted Answer

According to Faraday's Law of Induction, an emf is induced in a loop if there is a time-varying magnetic flux through the loop. The direction of the induced emf is given by Lenz's Law, which states that the emf is in a direction that opposes the change in magnetic flux that produced it.

In this case, the current in the long straight wire is decreasing with time. This means that the magnetic field produced by the wire is also decreasing with time, and therefore, the magnetic flux through the loops A, B, and C is changing.

Loop A is inside the decreasing magnetic field, and the current in the wire is decreasing. Therefore, the induced emf in loop A is in a direction that opposes the decrease in flux, which is clockwise. This is consistent with Lenz's Law.

Loop B is outside the decreasing magnetic field, and therefore, there is no change in magnetic flux through loop B. Hence, no emf is induced in loop B.

Loop C is inside the increasing magnetic field, which is produced when the current in the wire decreases. Therefore, the induced emf in loop C is in a direction that opposes the increase in flux, which is counterclockwise. This is consistent with Lenz's Law.

Thus, the correct choice is D) loop A has a counterclockwise emf, loop B has no induced emf, and loop C has a clockwise emf.

The Long Straight Wire in the Figure Carries a Current