The concentration of free electrons in silver is 5.85 ×10^28 per m^3. A strip of silver of thick

step 1 Alright, so we got some free electrons in some silver bar, strip of silver, there we go. We woul

The concentration of free electrons in silver is 5.85 ×10^28...

The concentration of free electrons in silver is $5.85 \times$ $10^{28}$ per $\mathrm{m}^{3}$. 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

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, it is the magnetic part of the Lorentz force—given by F = q(v × B)—that causes the lateral deflection of charge carriers, resulting in the building up of the transverse Hall voltage.

Hall Effect

The Hall effect is the phenomenon where a voltage difference (Hall voltage) appears across a conductor when a magnetic field is applied perpendicular to the current flow. This occurs due to the Lorentz force acting on moving charge carriers, which causes them to deflect and accumulate on one side of the conductor, thereby creating a potential difference.

Drift Velocity

Drift velocity is the average speed at which charge carriers, such as electrons, move through a conductor due to an applied electric field. It links the macroscopic current flowing through the material to the microscopic motion of its charge carriers, and is determined by the relation between current density, carrier density, and the charge of the carriers.

Current Density

Current density represents the amount of electric current flowing per unit cross-sectional area of a conductor. It is a crucial concept in relating the macroscopic current of a conductor to the microscopic drift velocity of its charge carriers through the equation J = nqv, where n is the carrier density, q is the elementary charge, and v is the drift velocity.

Free Electron Density

Free electron density refers to the number of conduction electrons available per unit volume in a material, typically a metal. This concept is central to understanding a material's electrical conductivity and is used in calculations that relate current, drift velocity, and the microscopic properties of the conductor.

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