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 electromagnetic induction, the induced emf in a closed loop is given by the rate of change of magnetic flux linked with the loop.

For loop A, as the current in the wire decreases with time, the magnetic field around the wire also decreases. This change in magnetic field induces an emf in loop A in such a way that it opposes the decrease in flux. This can be achieved by inducing a magnetic field around loop A which is directed in the clockwise direction. Therefore, loop A has a clockwise emf.

For loop B, as it is just a straight wire, it does not enclose any magnetic field and hence there is no change in flux linked with it. Therefore, no emf is induced in loop B.

For loop C, as the current in the wire decreases with time, the magnetic field around the wire also decreases. This change in magnetic field induces an emf in loop C in such a way that it opposes the decrease in flux. This can be achieved by inducing a magnetic field around loop C which is directed in the clockwise direction. Therefore, loop C has a clockwise emf.

Hence, the best choice is D: loop A has a counter-clockwise emf, loop B has no induced emf, and loop C has a clockwise emf.

The Long Straight Wire in the Figure Carries a Current