Question

What is the Hall voltage for drift velocity?

Answer 1

The Hall voltage is the voltage generated across a conductor when it carries an electric current and is placed in a magnetic field perpendicular to the direction of current flow. This voltage is produced due to the Lorentz force acting on the charge carriers (like electrons) inside the conductor, which causes them to accumulate on one side of the conductor.

The Hall voltage (\( V_H \)) can be related to the drift velocity (\( v_d \)) of the charge carriers through the following formula:

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

Where:

1. \( V_H \) is the Hall voltage
   

1. \( B \) is the magnetic field strength
   

1. \( I \) is the current flowing through the conductor
   

1. \( d \) is the thickness of the conductor (perpendicular to both current and magnetic field)
   

1. \( n \) is the number density of charge carriers
   

1. \( e \) is the charge of the carrier (for electrons, \( e \approx 1.6 \times 10^{-19} \, \text{C} \))
   

The Hall voltage is a result of the drift velocity of charge carriers, which causes a transverse deflection in the carriers when they move through the magnetic field, leading to a potential difference across the conductor.

To tie it to drift velocity specifically, you could express the number density \( n \) in terms of the drift velocity using:

\[
n = \frac{J}{e v_d}
\]

Where \( J \) is the current density. This provides a way to indirectly relate Hall voltage to the drift velocity of the carriers.

However, for most practical purposes, the formula for Hall voltage is often used directly as given above.