Question

What is the Hall voltage of a wire?

Answer 1

The Hall voltage is a small voltage that develops across a conductor (like a wire) when a magnetic field is applied perpendicular to the current flowing through the wire. This effect is called the Hall Effect, named after the American physicist Edwin Hall who discovered it in 1879.

How It Works:

1. Current Flow: When an electric current flows through a conductor, free electrons move in the direction of the current (or opposite, depending on how you define current).
   

1. Magnetic Field: If a magnetic field is applied perpendicular to the direction of the current, the magnetic force (Lorentz force) will push the moving charges to one side of the wire. This creates a charge buildup on one side of the conductor.
   

1. Hall Voltage: The charge separation causes an electric potential (voltage) to build up across the conductor, which is called the Hall voltage. This voltage is perpendicular to both the current and the magnetic field.
   

Formula for Hall Voltage:

The Hall voltage (\(V_H\)) can be calculated using the formula:

\[
V_H = \frac{B \cdot I \cdot d}{n \cdot A}
\]

Where:

1. \(B\) = Magnetic field strength (in tesla, T)
   

1. \(I\) = Current flowing through the wire (in amperes, A)
   

1. \(d\) = Thickness of the wire (in meters, m)
   

1. \(n\) = Charge carrier density (in \(m^{-3}\))
   

1. \(A\) = Cross-sectional area of the wire (in \(m^2\))
   

Key Points:

1. The Hall voltage is directly proportional to the magnetic field strength (\(B\)) and the current (\(I\)).
   

1. It is inversely proportional to the charge carrier density (\(n\)) and the cross-sectional area (\(A\)) of the wire.
   

  

Applications:

1. Measuring Magnetic Fields: The Hall effect can be used to measure magnetic fields, especially in sensors.
   

1. Determining Carrier Type: It helps to determine whether the charge carriers in the material are electrons (negative) or holes (positive), which is important in semiconductor research.
   

In short, the Hall voltage is a result of the interaction between current and magnetic fields, giving a useful way to measure magnetic fields and properties of materials.