Figure E 27.53 shows a portion of a silver ribbon with z ...

Figure $\mathrm { E } 27.53$ shows a portion of a silver ribbon with $z _ { 1 } = 11.8 \mathrm { mm } \quad$ and $\quad y _ { 1 } =$ 0.23$\mathrm { mm }$ , carrying a current of 120$\mathrm { A }$ in the $+ x$ -direction. The ribbon lies in a uniform magnetic field, in the $y$ -direction, with magnitude 0.95$\mathrm { T }$ Apply the simplified model of the Hall effect presented in Section $27.9 .$ If there are $5.85 \times 10 ^ { 28 }$ free electrons per cubic meter, find (a) the magnitude of the drift velocity of the electrons in the $x$ -direction; (b) the magnitude and direction of the electric field in the z-direction due to the Hall effect; (c) the Hall emf.

Figure $\mathrm { E } 27.53$ shows a portion of a silver ribbon with
$z _ { 1 } = 11.8 \mathrm { mm } \quad$ and $\quad y _ { 1 } =$
0.23$\mathrm { mm }$ , carrying a current of 120$\mathrm { A }$ in the $+ x$ -direction. The
ribbon lies in a uniform magnetic
field, in the $y$ -direction, with
magnitude 0.95$\mathrm { T }$ Apply the simplified model of the Hall effect
presented in Section $27.9 .$ If there are $5.85 \times 10 ^ { 28 }$ free electrons per cubic meter, find (a) the
magnitude of the drift velocity of the electrons in the $x$ -direction; (b)
the magnitude and direction of the electric field in the z-direction
due to the Hall effect; (c) the Hall emf.

Key Concepts

Drift Velocity

Drift velocity is the average velocity at which charge carriers, such as electrons, move through a conductor under the influence of an applied electric field. It is directly associated with the current flowing through the conductor and is determined by the carrier density and the charge of the carriers. In problems involving the Hall effect, the drift velocity is key to quantifying the current and the resulting Lorentz force on the charges.

Hall Voltage

Hall voltage is the potential difference generated across a conductor due to the separation of charge carriers as they experience the magnetic component of the Lorentz force. This voltage can be used to determine parameters like carrier density and the strength of the magnetic field, and it is central to devices that utilize the Hall effect for magnetic field sensing or current measurement.

Charge Carrier Density

Charge carrier density refers to the number of charge carriers, typically electrons in a metal, per unit volume. It is a crucial parameter in determining the electrical properties of the material, such as conductivity and the drift velocity of the carriers, and plays an important role in the quantitative analysis of the Hall effect.

Hall Effect

The Hall effect is the production of a transverse voltage (the Hall voltage) across a current?carrying conductor when it is placed in a magnetic field. This occurs because the magnetic field exerts a Lorentz force on the moving charge carriers, deflecting them to one side and creating a potential difference across the conductor perpendicular to both the magnetic field and the current flow.

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving in an electromagnetic field. In the context of the Hall effect, it is the magnetic component of this force that acts on the moving electrons, causing them to deflect to one side of the conductor. This deflection leads to the accumulation of charge and the creation of a transverse electric field.

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