The current I in a long, straight wire is constant and is...

The current $I$ in a long, straight wire is constant and is directed toward the right as in $\textbf{Fig. E29.16}$. Conducting loops $A$, $B$, $C$, and $D$ are moving, in the directions shown, near the wire. (a) For each loop, is the direction of the induced current clockwise or counterclockwise, or is the induced current zero? (b) For each loop, what is the direction of the net force that the wire exerts on the loop? Give your reasoning for each answer.

Key Concepts

Faraday's Law of Electromagnetic Induction

Faraday's law states that a changing magnetic flux through a closed loop induces an electromotive force (emf) in the loop. In cases where the loop is moving in a magnetic field, the flux through the loop changes over time, giving rise to a motional emf. This principle is used to determine the magnitude and direction of the induced current in moving loops.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of vectors in a magnetic context, such as the direction of the magnetic field around a current-carrying conductor or the direction of forces acting on moving charges. It is an essential tool for understanding and predicting the outcomes of interactions between currents, magnetic fields, and induced forces in electromagnetism.

Magnetic Force on Current-Carrying Conductors

When a conducting current-carrying loop is placed in a magnetic field, or when it moves through a magnetic field, it experiences a net force due to the interaction between the current in the loop and the external magnetic field. The direction of the force can be determined using an appropriate application of the Lorentz force law or by employing right-hand rules, and it is crucial for analyzing the dynamics of the loop's motion in relation to the source of the magnetic field.

Magnetic Field of a Current-Carrying Conductor

A current-carrying wire generates a magnetic field around it, the direction of which can be determined using the right?hand rule. The field forms concentric circles centered on the wire, with the magnitude of the field decreasing as the distance from the wire increases. This concept is essential to understanding the interactions between the wire and nearby moving conducting loops.

Lenz's Law

Lenz's law provides the direction of the induced current resulting from a changing magnetic flux by stating that the induced current will oppose the change in flux that produced it. The law is fundamental in predicting how a system will react to a change in magnetic environment, ensuring that the induced magnetic field counteracts the applied change.

Transcript

0:00 For a given problem.

00:01 We have following situation, it could and flows in a while towards the right here.

00:08 So the current flows in this direction, and due to this current, a magnetic field is produced.

00:14 And so the main t feel here below the wild point gets into there into the page.

00:22 We represented by cross here and here.

00:24 It gets out of the page we represented by adult.

00:28 Here we have four loops.

00:31 We have a loop a that moves away from the wire with the speed of e and fluke.

00:40 See here that moves a bandler to the current.

00:45 So this is see, we have a nuclear be here that moves away from the wire in this direction.

00:53 Re discreet to be and we have a little d that moves towards the wire.

01:01 So d here, you know, as we move away from the wire, the manti field decreases is we move towards the why the mayfield increases.

01:15 So the idea is re change our position with respect to the wire, the immunity field changes.

01:23 So for loop, eh? it moves farther from the wire.

01:28 So the man tick field according to the lenses law, the induce current in the loop must flow search today two opposed exterminating field toe oppose the decreasing in the 19 field they induce, mayfield must point out off the page.

01:47 Hence they induced current must flo a counter clockwise direction.

01:54 We have a similar situation in luke, baby, but the man tick field is in the position off.

02:02 A movie is into the page so the indians current must flow.

02:07 For this is for a the indians...

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