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To determine the direction of the induced current in the metallic loop when the electric current flows from B to A in the wire, we can apply Lenz's law.
Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.
In this case, when the current flows from B to A in the wire, it generates a magnetic field around the wire in the clockwise direction (using the right-hand grip rule). This magnetic field will intersect with the metallic loop.
Now, according to Faraday's law of electromagnetic induction, the change in magnetic flux through the loop induces an electromotive force (emf) and consequently an induced current.
To oppose the increase in the magnetic flux caused by the current flowing from B to A, the induced current in the metallic loop must generate its own magnetic field. By the right-hand rule, this induced magnetic field should be in the counterclockwise direction.
Therefore, the induced current in the metallic loop will flow in such a way that it generates a magnetic field in the counterclockwise direction, opposing the increase in magnetic flux caused by the current in the wire.
In summary, the induced current in the metallic loop will flow in the counterclockwise direction.
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