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 So firstly to calculate the magnitude of the EMF in the circuit, we know the EMF EMPEpsilon is e

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 - $\mathrm{T}$ magnetic field. The bar rides on parallel metal rails connected through a $25.0-\Omega$ resistor, as shown in $\mathrm{Fig}$ . 29.36 , so the apparatus makes a complete circuli. 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; (i) using Faraday's law; (iii) using Lenz's law. (c) Calculate the current through the resistor.

Key Concepts

Motional Electromotive Force (EMF)

This concept describes the voltage induced in a conductor when it moves through a magnetic field. The induced EMF arises because the moving charges experience a magnetic force, and it depends on the magnetic field strength, the speed of the conductor, and the length of the conductor within the field. It is a specific case of electromagnetic induction known as the motional EMF effect.

Faraday's Law of Electromagnetic Induction

Faraday's Law states that a changing magnetic flux through a circuit induces an electromotive force in that circuit. The law quantifies how the magnitude of the induced EMF is proportional to the rate at which the magnetic flux is changing with time, making it fundamental in understanding how time-varying magnetic fields generate electrical currents.

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving through a magnetic field. It is given by the cross product of the particle’s velocity and the magnetic field, which results in a force perpendicular to both. This principle explains why moving charges in a conductor experience a deflection, leading to the separation of charges and the creation of an induced voltage.

Lenz's Law

Lenz's Law provides the direction of the induced current and states that the induced current will flow in such a way as to oppose the change in magnetic flux that produced it. This negative feedback mechanism ensures the conservation of energy in electromagnetic systems by counteracting the cause of the induction.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits stating that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. It is used to calculate the current when the induced EMF and the resistance of the circuit are known.

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