A strip of copper is placed in a uniform magnetic field of...

A strip of copper is placed in a uniform magnetic field of magnitude 2.5 T. The Hall electric field is measured to be $1.5 \times 10^{-3} \mathrm{V} / \mathrm{m} .$ (a) What is the drift speed of the conduction electrons? (b) Assuming that $\mathrm{n}=8.0 \times 10^{28}$ electrons per cubic meter and that the cross-sectional area of the strip is $5.0 \times 10^{-6} \mathrm{m}^{2},$ calculate the current in the strip. (c) What is the Hall coefficient 1/nq?

Key Concepts

Electric Current in Conductors

Electric current in a conductor is the result of the movement of charge carriers, and it is directly proportional to both the drift velocity of those carriers and the cross-sectional area of the conductor. The relationship integrates the effect of charge carrier density and the individual charge of each carrier to determine the overall current flowing through the material.

Hall Effect

The Hall effect is the phenomenon whereby a voltage difference (Hall voltage) is produced across an electrical conductor transverse to an electric current in the conductor and a magnetic field perpendicular to the current. This effect arises due to the Lorentz force acting on the moving charge carriers, causing them to accumulate on one side of the conductor and create an electric field that opposes further charge separation.

Drift Velocity

Drift velocity refers to the average speed at which charge carriers, such as electrons, move through a conductor when subjected to an electric field. It is a critical parameter that links the microscopic motion of individual charge carriers to the macroscopic current observed in the conductor.

Charge Carrier Density

Charge carrier density is the number of charge carriers per unit volume within a material. In the context of electrical conduction, this parameter plays a fundamental role in determining electrical properties like conductivity and is essential for calculating the current and other related quantities in a conductor.

Hall Coefficient

The Hall coefficient is a parameter that quantifies the magnitude of the Hall effect in a material. It is defined as the ratio of the induced Hall electric field to the product of the magnetic field and the current density. Fundamentally, it is inversely proportional to the charge carrier density and the charge of the carriers, and it provides key insights into the type and density of the carriers within the material.

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