Question

A loop of copper wire is lying flat on a horizontal table. A bar magnet is held above the center of the loop with its south pole downward. The magnet is moved toward the loop. As viewed from above, what is the direction of the current induced in the loop as the magnet approaches the loop?

Answer 1

The current induced in the loop of copper wire as the south pole of the bar magnet moves toward it will flow counterclockwise when viewed from above.

Step-by-step explanation:

When a magnet is moved toward a conducting loop, Faraday's law of electromagnetic induction comes into play. According to this law, a changing magnetic field induces an electromotive force (EMF) in a conductor. In this scenario, as the south pole of the magnet moves closer to the loop, it induces a changing magnetic field through the loop. This changing magnetic field creates an EMF that drives a current in the loop to produce a magnetic field opposing the change that caused it.

Using the right-hand rule, the induced current direction can be determined. As the south pole of the magnet approaches the loop, a magnetic field through the loop is induced. This changing magnetic field induces a counterclockwise current flow in the loop, creating a magnetic field opposing the magnet's approach. The induced current generates its own magnetic field, following Lenz's law, to counteract the change in the external magnetic field. The direction of the induced current opposes the change in the magnetic field caused by the approaching south pole of the magnet.

Mathematically, Faraday's law states that the induced EMF is proportional to the rate of change of magnetic flux through the loop. The induced EMF (ε) is given by ε =
`(dФ)/(dt)`, where (Φ) is the magnetic flux. In this scenario, the changing magnetic field induces a negative rate of change in magnetic flux, resulting in an induced current that flows counterclockwise to oppose the approaching magnet.