Consider the arrangement shown in Figure P31.20. Assume that...

Consider the arrangement shown in Figure P31.20. Assume that $R=6.00 \Omega, \ell=1.20 \mathrm{~m}$, and a uniform 2.50-T magnetic field is directed into the page. At what speed should the bar be moved to produce a current of $0.500 \mathrm{~A}$ in the resistor?

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Key Concepts

Motional Electromotive Force

This concept explains that when a conductor moves in a magnetic field, the free charges inside it experience a magnetic force (Lorentz force) that separates them along the length of the conductor, creating a potential difference or electromotive force (emf). This induced emf is directly proportional to the magnetic field strength, the length of the conductor, and its velocity relative to the field.

Faraday's Law of Electromagnetic Induction

Faraday's Law states that a change in magnetic flux through a circuit induces an electromotive force in that circuit. In scenarios where a conductor moves in a uniform magnetic field, the change in magnetic flux is due to the movement of the conductor, and the induced emf can be calculated by considering the area swept out, leading to the same result as the motional emf equation.

Ohm's Law

Ohm's Law is a fundamental principle that relates voltage (or emf), current, and resistance in an electrical circuit through the equation I = V/R. In problems involving induced emf, Ohm's Law is used to connect the induced voltage created by electromagnetic induction to the current flowing in the circuit, thereby allowing the determination of unknown quantities such as the required speed of motion.

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