A long straight wire and a plane rectangular conducting loop are both on the xy plane. The wire is along the y axis, and the loop lies in the x>0 semiplane, with edges parallel to the coordinated axis. The straight wire carries a current, directed downward, which is decreasing in magnitude. The current induced in the rectangle as a result is
a. zero
b. directed leftward in both of the edges parallel to the x axis
c. clockwise
d. counterclockwise
e. directed upward in both of the edges parallel to the y axis
Question
Answer:
c. clockwise
Explanation:
This is because, the magnetic field, B produced due to the downward flowing current in the straight wire is perpendicular to the plane of the rectangular conducting loop and directed outwards from it.
Since it also decreases as it goes from the top of the loop to the bottom of the loop (and also from left to right since B ∝ 1/r), there is a change in magnetic flux which is negative, and thus and induced emf or current is generated to oppose this change in magnetic flux which is generating the current according to Lenz’s law. To generate a magnetic field in the opposite direction to that due to the straight wire, a current flowing in the clockwise direction must be generated in the loop.
So the answer is C. clockwise.