Strip of Copper A strip of copper 150 μm wide is placed in a uniform magnetic field B⃗ of magnit

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Strip of Copper A strip of copper 150 μm wide is placed in a...

Strip of Copper A strip of copper $150 \mu \mathrm{m}$ wide is placed in a uniform magnetic field $\vec{B}$ of magnitude $0.65 \mathrm{~T}$, with $\vec{B}$ perpendicular to the strip. A current $i=23 \mathrm{~A}$ is then sent through the strip such that a Hall potential difference $\Delta V$ appears across the width of the strip. Calculate $\Delta V$.(The number of charge carries per unit volume for copper is $8.47 \times 10^{2 \mathrm{~s}}$ electrons/m $^{3}$.)

Key Concepts

Current Density

Current density, defined as the electric current per unit cross-sectional area of the conductor, provides a measure of how densely the charge carriers move through the material. It is an important parameter in analyzing the Hall effect because it helps relate the macroscopic current to the microscopic motion (drift velocity) of the individual electrons.

Charge Carrier Density

Charge carrier density refers to the number of charge carriers per unit volume in a material. It plays a crucial role in determining how the applied current translates into drift velocity and, consequently, how effectively the magnetic field can induce a Hall voltage across the conductor.

Drift Velocity

Drift velocity is the average velocity at which charge carriers, such as electrons, move through a conductor under the influence of an electric field. It is directly related to the current flowing through the conductor and is essential in determining the magnitude of the Hall voltage since the Hall electric field is proportional to this velocity.

Lorentz Force

The Lorentz force is the force experienced by a moving charged particle in the presence of electric and magnetic fields. In the context of the Hall effect, the magnetic part of the Lorentz force deflects moving charge carriers sideways, which leads to charge separation and the creation of a measurable Hall voltage.

Hall Effect

The Hall effect is the production of a transverse voltage across a conductor when a current flows through it and the conductor is placed in a magnetic field perpendicular to the current. This voltage results from the deflection of charge carriers by the magnetic field, causing an accumulation of positive and negative charges on opposite sides of the material.

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