Let Fig. E27. 53 represent a strip of an unknown metal of...

Let Fig. E27. 53 represent a strip of an unknown metal of the same dimensions as those of the silver ribbon in Exercise 27.53 . When the magnetic field is 2.29$\mathrm { T }$ and the current is 78.0$\mathrm { A }$ , the Hall emf is found to be 131$\mu \mathrm { V }$ . What does the simplified model of the Hall effect presented in Section 27.9 give for the density of free electrons in the unknown metal?

Let Fig. E27. 53 represent a strip of an unknown metal of the same dimensions as those of the silver ribbon in Exercise 27.53 .
When the magnetic field is 2.29$\mathrm { T }$ and the current is 78.0$\mathrm { A }$ , the
Hall emf is found to be 131$\mu \mathrm { V }$ . What does the simplified model
of the Hall effect presented in Section 27.9 give for the density of
free electrons in the unknown metal?

Key Concepts

Lorentz Force

The Lorentz force is the force on a charged particle due to electromagnetic fields, given by the cross product of the particle's velocity and the magnetic field. This force is responsible for deflecting the charge carriers in a conductor, which is the fundamental mechanism behind the Hall effect.

Hall Coefficient

The Hall coefficient is a parameter derived from measurements of the Hall effect that relates the Hall voltage to the product of the current, magnetic field, and sample geometrical factors. It is used to determine the concentration and nature (positive or negative) of the charge carriers in the material.

Free Electron Density

Free electron density is the concentration of conduction electrons available in a material that can respond to external electric fields. Determining this density is key in solid-state physics because it directly affects electrical conductivity and can be measured using the Hall effect.

Hall Effect

The Hall effect is the phenomenon in which a transverse voltage develops across an electrical conductor when it carries an electric current in a perpendicular magnetic field. This voltage arises because the magnetic field exerts a Lorentz force on the moving charge carriers, causing them to accumulate on one side of the material and thereby creating a potential difference.

Drift Velocity

Drift velocity is the average velocity attained by charged particles, such as electrons, in a conductor due to an applied electric field. It links the macroscopic current flow to the microscopic movement of charge carriers and is crucial for relating current density to the resulting Hall voltage.

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