Two closed loops A and C are close to a long wire carrying a...

Two closed loops $A$ and $C$ are close to a long wire carrying a current $I$ ($\textbf{Fig. E29.17}$). (a) Find the direction (clockwise or counterclockwise) of the current induced in each loop if $I$ is steadily decreasing. (b) While $I$ is decreasing, what is the direction of the net force that the wire exerts on each loop? Explain how you obtain your answer.

Key Concepts

Magnetic Dipole Interaction

A current loop behaves as a magnetic dipole, and its interaction with an external magnetic field, such as that produced by a long current-carrying wire, results in forces that can be attractive or repulsive. The net force on the loop depends on the relative orientations of its magnetic dipole moment and the external field gradient, which is crucial for determining the direction of the force on the loop as the magnetic field from the wire changes.

Lenz's Law

Lenz's Law provides the direction of the induced current by stating that the induced current will flow in such a way as to oppose the change in magnetic flux that produced it. This opposition ensures the conservation of energy and explains why the induced current in the loops flows in a direction that attempts to counteract the decrease or increase in the magnetic field from the nearby wire.

Faraday's Law of Electromagnetic Induction

This principle states that a changing magnetic flux through a closed loop induces an electromotive force (EMF) in the loop. The amount of induced EMF is proportional to the rate at which the magnetic flux changes, and this concept is central to understanding how currents can be generated in loops situated near dynamic magnetic fields.

Right-Hand Rule

The Right-Hand Rule is a technique used to determine the direction of the magnetic field relative to the direction of current flow. It is also used to relate the direction of force, magnetic field, and current in a conductor. This rule is particularly useful when analyzing the magnetic field around a current-carrying wire and the resulting forces acting on nearby currents or magnetic dipoles.

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