A 1.50 -m-long metal bar is pulled to the right at a steady 5.0 m / s perpendicular to a uniform

step 1 Hi, in the given problem, 1 .50 meter long metal bar is moving over the parallel rails. The leng

A 1.50 -m-long metal bar is pulled to the right at a steady...

A 1.50 -m-long metal bar is pulled to the right at a steady 5.0 $\mathrm{m} / \mathrm{s}$ perpendicular to a uniform, 0.750 -T magnetic field. The bar rides on parallel metal railsconnected through a $25.0-\Omega$ resistor, as shown in Fig. E29.28, so the apparatus makes a complete circuit. You can ignore the resistance of the bar and the rails. (a) Calculate the magnitude of the emf induced in the circuit. (b) Find the direction of the current induced in the circuit (i) using the magnetic force on the charges in the moving bar; (ii) using Faraday's law; (iii) using Lenz's law. (c) Calculate the current through the resistor.

A 1.50 -m-long metal bar is pulled to the right at a steady 5.0 $\mathrm{m} / \mathrm{s}$ perpendicular to a uniform, 0.750 -T magnetic field. The bar rides on parallel metal railsconnected through a $25.0-\Omega$ resistor, as shown in Fig. E29.28, so the apparatus makes a complete circuit. You can ignore the resistance of the bar and the rails. (a) Calculate the magnitude of the emf induced in the circuit.
(b) Find the direction of the current induced in the circuit (i) using the magnetic force on the charges in the moving bar; (ii) using Faraday's law; (iii) using Lenz's law. (c) Calculate the current through the resistor.

Key Concepts

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in a magnetic field, given by F = q(v × B). In the context of a moving conductor, the free charges within the material experience this force, which pushes them to one side of the bar, creating a potential difference. This explanation is used to determine the direction of the induced emf or current.

Lenz's Law

Lenz's law provides the direction of the induced current resulting from a change in magnetic flux. It states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it. This conservation of energy and opposition is crucial for understanding the feedback effect in electromagnetic systems.

Ohm's Law

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points, I = V/R. Once the induced emf is calculated, Ohm's law allows for the determination of the current in the circuit by accounting for the resistance present.

Motional EMF

This refers to the electromotive force generated when a conductor moves through a magnetic field. The induced emf is calculated using the relationship ? = B?v, where B is the magnetic field strength, ? is the length of the conductor, and v is its velocity. It is a key concept in understanding generators and currents induced by motion.

Faraday's Law

Faraday's law of electromagnetic induction states that a changing magnetic flux through a circuit induces an electromotive force. In the context of a moving conductor, the movement causes a change in flux, giving rise to the induced emf. This principle underlies the operation of many electrical devices and explains how mechanical motion can be converted into electrical energy.

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