Some metal alloy is known to have electrical conductivity...

Some metal alloy is known to have electrical conductivity and electron mobility values of $1.2 \times 10^{7}(\Omega-\mathrm{m})^{-1}$ and $0.0050 \mathrm{m}^{2} / \mathrm{N}-\mathrm{s}$, respec- tively. Through a specimen of this alloy that is $35 \mathrm{mm}$ thick is passed a current of $40 \mathrm{A}$. What magnetic field would need to be imposed to yield a Hall voltage of $-3.5 \times 10^{-7} \mathrm{V} ?$

Some metal alloy is known to have electrical conductivity and electron mobility values of $1.2 \times 10^{7}(\Omega-\mathrm{m})^{-1}$ and $0.0050 \mathrm{m}^{2} / \mathrm{N}-\mathrm{s}$, respec-
tively. Through a specimen of this alloy that is $35 \mathrm{mm}$ thick is passed a current of $40 \mathrm{A}$. What magnetic field would need to be imposed to yield a Hall voltage of $-3.5 \times 10^{-7} \mathrm{V} ?$

Key Concepts

Hall Effect

The Hall effect is the phenomenon where a voltage difference, known as the Hall voltage, is generated across an electrical conductor when a magnetic field is applied perpendicular to the direction of the current flow. This effect arises because the magnetic field exerts a transverse force on the moving charge carriers, causing them to deflect and accumulate on one side of the conductor. The Hall effect is widely used to measure magnetic field strength, charge carrier density, and the type of charge carriers in a material.

Electron Mobility

Electron mobility is a measure of how quickly electrons can move through a conductor or semiconductor when subjected to an electric field. Higher mobility means that the charge carriers can respond more rapidly to the applied field, resulting in greater current for a given voltage. Mobility is crucial for understanding and predicting the behavior of charge carriers under applied forces, and it plays a significant role in determining both the electrical conductivity and the response of materials to magnetic fields in phenomena such as the Hall effect.

Electrical Conductivity

Electrical conductivity quantifies a material's ability to conduct electric current and reflects how easily charge carriers can flow through the material. It is influenced by the density and mobility of the charge carriers, as well as other factors like the scattering of these carriers by impurities and lattice vibrations. In the context of the Hall effect, electrical conductivity is important because it helps relate the net current flow to the internal forces acting on the carriers, ultimately affecting the measurement of the induced Hall voltage.

Lorentz Force

The Lorentz force is the force experienced by a charged particle moving in the presence of electric and magnetic fields. In a magnetic field, this force acts perpendicular to both the particle's velocity and the magnetic field, causing the charge carriers to be deflected sideways. This deflection of carriers is the fundamental mechanism behind the Hall effect, as it leads to the development of the transverse voltage across the conductor.

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