A metal bar spins at a constant rate in the magnetic field...

A metal bar spins at a constant rate in the magnetic field of the Earth as in Figure $31.10$. The rotation occurs in a region where the component of the Earth's magnetic field perpendicular to the plane of rotation is $3.30 \times 10^{-5} \mathrm{~T}$. If the bar is $1.00 \mathrm{~m}$ in length and its angular speed is $5.00 \pi \mathrm{rad} / \mathrm{s}$, what potential difference is developed between its ends?

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Key Concepts

Electromagnetic Induction

This concept involves generating an electromotive force (emf) in a conductor due to a change in magnetic flux, as described by Faraday's Law. It applies broadly to situations where either the magnetic field, the area of a loop, or the orientation between them changes over time.

Motional EMF

Motional emf refers to the voltage induced in a conductor as it moves through a magnetic field. When a conductor moves relative to a magnetic field, the charges within the conductor experience the Lorentz force, which separates them and creates a potential difference along the length of the conductor.

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in a magnetic field. This force acts perpendicular to both the direction of the particle's velocity and the magnetic field, and it is fundamental to understanding how motion in a magnetic field can produce an induced emf in a conductor.

Rotational Motion in Magnetic Fields

When a conductor rotates in a magnetic field, different parts of the conductor move at different linear speeds, which leads to a non-uniform distribution of the Lorentz force along its length. This concept is essential for analyzing cases where the induced emf is calculated by integrating the contributions of infinitesimal segments of the rotating conductor.

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