A 0.250-m-long bar moves on parallel rails that are...

A 0.250-m-long bar moves on parallel rails that are connected through a 6.00-$\Omega$ resistor, as shown in $\textbf{Fig. E29.33}$, so the apparatus makes a complete circuit. You can ignore the resistance of the bar and rails. The circuit is in a uniform magnetic field $B =$ 1.20 T that is directed into the plane of the figure. At an instant when the induced current in the circuit is counterclockwise and equal to 1.75 A, what is the velocity of the bar (magnitude and direction)?

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Key Concepts

Faraday's Law of Induction

This principle states that a changing magnetic flux through a closed circuit induces an electromotive force (emf) in the circuit. It is a central concept in electromagnetism which explains how moving a conductor in a magnetic field or changing the field around a conductor generates an emf.

Motional Electromotive Force (EMF)

Motional emf is the voltage generated when a conductor moves through a magnetic field. The magnitude of the induced emf is given by the product of the magnetic field strength, the length of the conductor, and its velocity relative to the magnetic field, illustrating how mechanical movement can be converted into electrical energy.

Ohm's Law

Ohm's Law relates the voltage across a conductor to the current flowing through it and the resistance of the conductor. In circuits where motional emf is generated, Ohm's law enables one to determine the current (or velocity, when combined with the emf formula) by relating the induced emf and the total resistance in the circuit.

Lenz's Law

Lenz's Law is used to determine the direction of the induced current such that it opposes the change in magnetic flux that produced it. It is fundamental for understanding the feedback mechanism in electromagnetic induction, ensuring conservation of energy in the system.

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