Hall resistivity is a physical phenomenon that occurs when a current-carrying conductor is placed in a magnetic field. It arises due to the deflection of charge carriers, such as electrons, by the magnetic field, resulting in the development of a potential difference perpendicular to both the current and the magnetic field.
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The Hall resistivity is proportional to the strength of the magnetic field and the current flowing through the conductor.
The sign of the Hall resistivity indicates the type of charge carriers (positive or negative) responsible for the current flow.
Hall resistivity is used to determine the carrier concentration and mobility in semiconductors and other materials.
The Hall effect is the basis for the operation of Hall-effect sensors, which are used in a variety of applications, such as magnetic field measurement and current sensing.
The magnitude of the Hall resistivity is inversely proportional to the density of charge carriers in the material.
Review Questions
Explain how the Hall effect leads to the development of Hall resistivity in a current-carrying conductor placed in a magnetic field.
When a current-carrying conductor is placed in a magnetic field, the magnetic field exerts a force (the Lorentz force) on the moving charge carriers, causing them to deflect in a direction perpendicular to both the current and the magnetic field. This deflection of the charge carriers results in the accumulation of charge on one side of the conductor, creating a potential difference across the conductor, known as the Hall voltage. The ratio of this Hall voltage to the current and the magnetic field strength is defined as the Hall resistivity, which is a characteristic property of the material and can be used to determine the properties of the charge carriers, such as their concentration and mobility.
Describe how the Hall resistivity can be used to determine the type and concentration of charge carriers in a material.
The sign of the Hall resistivity indicates the type of charge carriers (positive or negative) responsible for the current flow. If the Hall resistivity is positive, it indicates that the dominant charge carriers are positive (such as holes in a semiconductor), while a negative Hall resistivity indicates that the dominant charge carriers are negative (such as electrons in a metal). Additionally, the magnitude of the Hall resistivity is inversely proportional to the density of charge carriers in the material. By measuring the Hall resistivity and the current-voltage characteristics of a material, it is possible to determine the concentration and mobility of the charge carriers, which are important parameters in understanding the electrical properties of the material.
Explain the importance of the Hall effect and Hall resistivity in practical applications, such as the operation of Hall-effect sensors.
The Hall effect and the resulting Hall resistivity are the fundamental principles behind the operation of Hall-effect sensors, which are widely used in various applications. Hall-effect sensors can be used to measure magnetic field strength, detect the presence of magnetic materials, and sense electric current. These sensors are employed in a variety of devices, including compass modules, brushless DC motor controllers, and current transformers. The ability to determine the type and concentration of charge carriers through Hall resistivity measurements also makes it a valuable tool in the characterization of semiconductor materials and devices, which are essential components in modern electronics and technology.
Related terms
Hall Effect: The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current.
Lorentz Force: The Lorentz force is the combination of electric and magnetic force that acts on a charged particle moving in an electromagnetic field.
Charge Carriers: Charge carriers are the particles that carry electric charge and are responsible for the flow of electric current in a material, such as electrons in metals or holes in semiconductors.