An airplane propeller of total length L rotates around its...

An airplane propeller of total length $L$ rotates around its center with angular speed $\omega$ in a magnetic field that is perpendicular to the plane of rotation. Modeling the propeller as a thin, uniform bar, find the potential difference between (a) the center and either end of the propeller and (b) the two ends. (c) If the field is the earth's field of 0.50 G and the propeller turns at 220 rpm and is 2.0 m long, what is the potential difference between the middle and either end? It this large enough to be concerned about?

Key Concepts

Electromagnetic Induction

This concept describes how a voltage (or electromotive force) is generated in a conductor when it experiences a change in magnetic flux. In the context of the problem, as the propeller rotates in a constant magnetic field, different parts of the propeller cut through magnetic field lines at varying speeds, inducing a potential difference along its length.

Motional Electromotive Force (emf)

Motional emf arises when a conductor moves through a magnetic field, causing free charge carriers within the conductor to experience a force and accumulate at one end. The induced emf is proportional to the magnetic field strength, the velocity of the conductor, and the effective length over which the field is experienced.

Lorentz Force

The Lorentz force is the force experienced by a moving charge in a magnetic field. It is given by F = q(v × B) and is responsible for pushing charge carriers in the conductor to accumulate at one end during motion. This accumulation results in a measurable potential difference.

Rotational Motion and Linear Velocity Conversion

In rotating systems, different points along a rotating object have different tangential speeds, which are related to the angular velocity by the relation v = ?r. This concept is crucial for analyzing the induced emf in different parts of the rotating propeller, as the potential difference depends on the local speed at each point along its length.

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