In Fig. 28-8, show that the ratio of the Hall electric field...

In Fig. $28-8$, show that the ratio of the Hall electric field magnitude $E$ to the magnitude $E_{C}$ of the electric field responsible for moving charge (the current) along the length of the strip is $$ \frac{E}{E_{C}}=\frac{B}{n e \rho} $$ where $\rho$ is the resistivity of the material and $n$ is the number density of the charge carriers. (b) Compute this ratio numerically for Problem 13. (See Table 26-1.)

In Fig. $28-8$, show that the ratio of the Hall electric field magnitude $E$ to the magnitude $E_{C}$ of the electric field responsible for moving charge (the current) along the length of
the strip is
$$
\frac{E}{E_{C}}=\frac{B}{n e \rho}
$$
where $\rho$ is the resistivity of the material and $n$ is the number density of the charge carriers. (b) Compute this ratio numerically for Problem 13. (See Table 26-1.)

Key Concepts

Charge Carrier Density

Charge carrier density is the concentration of charge carriers (such as electrons) per unit volume in a material. This parameter is crucial in determining the material’s conductivity and directly affects the magnitude of the Hall voltage, as it determines how many charges are available to be deflected by the magnetic field.

Resistivity

Resistivity is a fundamental property of materials that quantifies how strongly they oppose the flow of electric current. It links the applied electric field to the resulting current density via Ohm’s law, and in the context of the Hall effect, it influences the magnitude of the current-driving electric field required to maintain a given current.

Electric Field and Current Drive

The electric field responsible for driving the current (denoted as E_C) is directly related to the current density and the material's resistivity via Ohm's law. Understanding the balance between this driving electric field and the Hall electric field is essential to analyze how a magnetic field affects charge carriers in a conductor.

Hall Effect

The Hall effect is the phenomenon in which a transverse voltage (the Hall voltage) is developed across a conductor when it carries a current in the presence of a perpendicular magnetic field. This arises from the magnetic force (Lorentz force) acting on moving charge carriers, which causes them to accumulate on one side of the conductor, thereby establishing an electric field.

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 component of the Lorentz force that deflects the charge carriers, leading to the buildup of a transverse electric field across the conductor.

Transcript

Please give Ace some feedback