A long, vertical, straight wire carries a current I going upwards. The wire is perpendicular to the plane of a circular metal loop and passes through the center of the loop. The loop is allowed to fall and maintains its orientation with respect to the straight wire while doing so. Is there an induced current in the loop? If so, in what direction does the current induced in the loop flow?
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A particle of charge +q and mass m is initially launched at speed v in a region with a constant, uniform magnetic field of magnitude B. If the particle launched in a direction perpendicular to the magnetic field, by the time the particle has traveled a distance d, the work done by the magnetic force on the particle is equal to:
Yes, there will be an induced current in the loop. According to Faraday's law of electromagnetic induction, a changing magnetic field through a loop of wire induces an electromotive force (EMF) in the loop, which in turn leads to an induced current.
In this scenario, when the wire carrying the current I is perpendicular to the plane of the loop and passes through its center, the changing magnetic field is produced due to the falling of the loop. As the loop falls, the distance between the wire and the loop decreases, causing a change in the magnetic field through the loop.
To determine the direction of the induced current, you can use the right-hand rule. Assuming the loop is circular and viewed from above, where the current-carrying wire passes through the center, point your thumb in the direction of the current I (which is upwards), and curl your fingers toward the center of the loop. The direction in which your fingers curl represents the direction of the induced current in the loop.
In this case, the induced current in the loop will flow counterclockwise (or anticlockwise) when viewed from above.