The number density of free electrons in silver is 5.85 ×10^28 m^-3 . A strip of silver of thickn

step 1 In this question, we're told we have a strip of silver. It is 0 .05 millimeters thick and 20 mil

The number density of free electrons in silver is 5.85...

The number density of free electrons in silver is $5.85 \times 10^{28} \mathrm{m}^{-3} .$ A strip of silver of thickness $0.050 \mathrm{mm}$ and width $20.0 \mathrm{mm}$ is placed in a magnetic field of $0.80 \mathrm{T} .$ A current of $10.0 \mathrm{A}$ is sent down the strip. (a) What is the drift velocity of the electrons? (b) What is the Hall voltage measured by the meter? (c) Which side of the voltmeter is at the higher potential?

The number density of free electrons in silver is $5.85 \times 10^{28} \mathrm{m}^{-3} .$ A strip of silver of thickness $0.050 \mathrm{mm}$
and width $20.0 \mathrm{mm}$ is placed in a magnetic field of $0.80 \mathrm{T} .$ A current of $10.0 \mathrm{A}$ is sent down the strip.
(a) What is the drift velocity of the electrons?
(b) What is the Hall voltage measured by the meter?
(c) Which side of the voltmeter is at the higher potential?

Key Concepts

Hall Effect

The Hall effect occurs when a current-carrying conductor is exposed to a perpendicular magnetic field, resulting in a transverse force on the moving charges that deflects them to one side of the conductor. This accumulation of charge on one side leads to a measurable voltage difference across the conductor, known as the Hall voltage. The effect is instrumental in determining the sign of the charge carriers and evaluating material properties such as carrier density and mobility.

Lorentz Force

The Lorentz force is the force exerted on a moving charged particle when it travels through a region with a magnetic field. This force, which acts perpendicular to both the velocity of the charge and the magnetic field, plays a key role in phenomena like the Hall effect by causing a deflection of charge carriers in a conducting material.

Charge Carrier Density

Charge carrier density indicates the number of free charge carriers, such as electrons, present in a unit volume of a material. This concept is critical in relating the physical properties of the material, such as its conductivity, to the microscopic dynamics of charge transport within the material.

Drift Velocity

Drift velocity refers to the average velocity that charge carriers, such as electrons, acquire in response to an electric field in a conductor. It is distinct from the random thermal motion of electrons and is calculated by relating the macroscopic current to the microscopic movement of carriers, taking into account the number density of the charge carriers and the cross-sectional area through which the current flows.

Current Density

Current density is a measure of the electric current per unit cross-sectional area of a conductor. It connects the macroscopic current to the microscopic behavior of charge carriers, enabling the calculation of drift velocity by dividing the current by the product of the carrier density, charge of the carriers, and the conductor's area.

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