Three conducting loops are situated side-by-side in the plane of the page. A clockwise current flows in the center loop B, and its magnitude is decreasing in time.
The induced currents in loops A and C:
flow in opposite directions (A clockwise, B counterclockwise) both flow counterclockwise both flow clockwise flow in opposite directions (A counterclockwise, B clockwise
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When a magnetic field changes in magnitude or direction, an electromotive force (EMF) is induced in nearby conducting loops according to Faraday's law of electromagnetic induction. The direction of the induced current in a loop can be determined using Lenz's law, which states that the induced current opposes the change in magnetic flux.
In this scenario, a clockwise current is flowing in loop B, and its magnitude is decreasing in time.
According to Lenz's law:
- Loop A will have an induced current that flows in the opposite direction of the change in magnetic flux caused by the decreasing current in loop B. Since the current in loop B is decreasing clockwise, the induced current in loop A will flow clockwise.
- Loop C will also have an induced current that flows in the opposite direction of the change in magnetic flux caused by the decreasing current in loop B. Therefore, the induced current in loop C will flow counterclockwise.
Therefore, the correct answer is: The induced currents in loops A and C flow in opposite directions. Specifically, the induced current in loop A flows clockwise, while the induced current in loop C flows counterclockwise.
To determine the directions of the induced currents in loops A and C, we can apply Lenz's law. Lenz's law states that the direction of an induced current is such that it opposes the change that caused it.
Since the current in loop B is decreasing, the magnetic field generated by this current is also decreasing. According to Faraday's law of electromagnetic induction, a decreasing magnetic field induces a current in loops A and C.
Let's consider loop A first. To determine the direction of the induced current in loop A, we can use the right-hand rule. Place your right hand (palm facing the plane of the page) with your fingers pointing in the direction of the magnetic field caused by the current in loop B. When the field decreases, your thumb will point in the direction of the induced current.
Now, let's move to loop C. Again, use the right-hand rule with your fingers pointing in the direction of the magnetic field caused by the current in loop B. As the field decreases, your thumb will point in the opposite direction of loop A's current.
Therefore, the induced current in loop A will flow clockwise, and the induced current in loop C will flow counterclockwise. Hence, the correct answer is: flow in opposite directions (A clockwise, B counterclockwise).