1 Answer
The Hall voltage is the voltage that develops across a conductor when it carries an electric current and is placed in a magnetic field. It arises due to the magnetic force acting on the moving charge carriers (like electrons) inside the material.
Here's how it works:
The Hall voltage (\(V_H\)) is given by the formula:
\[
V_H = \frac{B I t}{n e}
\]
Where:
Key Points:
In metals, the charge carriers are typically electrons, so the Hall voltage will give us insights into how the electrons are behaving in a magnetic field.
Here's how it works:
- When a metal or any conductor with current flowing through it is placed in a magnetic field, the moving charge carriers experience a force (called the Lorentz force) that pushes them to one side of the material. This causes a build-up of charges on that side.
- This charge separation creates a voltage difference across the material in the direction perpendicular to both the current and the magnetic field. This voltage is called the Hall voltage.
The Hall voltage (\(V_H\)) is given by the formula:
\[
V_H = \frac{B I t}{n e}
\]
Where:
- \(V_H\) = Hall voltage
- \(B\) = Magnetic field strength (in Tesla)
- \(I\) = Current passing through the material (in Amperes)
- \(t\) = Thickness of the material (in meters)
- \(n\) = Carrier density (number of charge carriers per unit volume)
- \(e\) = Charge of an electron (\(1.6 \times 10^{-19}\) Coulombs)
Key Points:
- The Hall voltage is dependent on the material's properties (like carrier density \(n\)) and external factors (like the magnetic field \(B\)).
- The direction of the Hall voltage can tell you about the type of charge carriers in the material. If the voltage is positive, the material has positive charge carriers (like holes in semiconductors), and if negative, it has negative charge carriers (like electrons in metals).
In metals, the charge carriers are typically electrons, so the Hall voltage will give us insights into how the electrons are behaving in a magnetic field.