# PHYS 2212 Module 7.6

## The Hall Effect

7.6 The Hall Effect

### Learning Objectives

By the end of this section, you will be able to:

• Explain a scenario where the magnetic and electric fields are crossed and their forces balance each other as a charged particle moves through a velocity selector
• Compare how charge carriers move in a conductive material and explain how this relates to the Hall effect

Imagine you have a battery and a conducting wire and connect the terminals of the battery like this:

We know that the conventional current will flow in this clockwise direction based on the orientation of the battery. And we also know that the particles that carry the charge are the electrons because electrons can move freely in a conductor. But in the 1800s, people didn’t know this. (This was before people even knew that electrons existed!) People at this time asked the question: Is this current (I) due to positive charges moving to the left or negative charges moving to the right?

In 1879, Edwin Hall (a graduate student in physics) used a magnetic field to manipulate the charge carriers in a strip of gold foil. He was able to show that the current is actually negative charges in motion. After this, he received a professorship at the university where he was a graduate student.

### The Hall Effect

Let’s walk through this experiment. Hall replaced the wire with a conducting ribbon, which is like a wire only flat and wide. And then he placed that conducting ribbon in a uniform magnetic field (represented by the X’s in the picture below — think: what is the direction of B?). When he connected the battery, a current flowed through the ribbon. He wanted to know, is this current made from positive charges moving to the left:

or negative charges moving to the right:

In this video, I explain the Hall experiment and what he found:

Practice!

### The Hall Voltage

In this picture, a current in flowing through the conducting ribbon. But as this current flows, the magnetic force separates the positive and negative charges so that there is a potential difference (voltage) across the top and bottom of the ribbon. This potential difference gives rise to an electric field between the separated charges. And this electric field exerts a force on the charges that is opposite to the magnetic force. The magnetic force is pushing downward on the electrons and the electric force is pushing them upwards.

These opposing forces reach an equilibrium such that FB = FE. If we set these two forces equal, we can solve for the Hall voltage. Recall that the magnetic force is FB = qvB and the electric force is qE, where E = ΔV/w (w is the width of the ribbon, and how far apart the charges are separated). So we get:

where v is the speed of the charges, B is the magnetic field strength, and w is the width of the conducting ribbon.