Tutorial 3B  Hall Effect 

Learning Objectives 
To study the Hall Effect. To derive the Hall equation. 

Key Questions 
What is the Hall Effect? How is it used? 

The Hall Effect It was first discovered in 1879 by an American Physicist, Edwin Herbert Hall (1855  1938). He found that when a currentcarrying conductor or a semiconductor is placed in a magnetic field, a voltage occurs that is perpendicular to the flow of the current. This is called the Hall Voltage.
The Hall Effect can be observed in conductors, semiconductors, ionised gases, and plasmas. We will be looking at the effect of magnetic fields in electrons in semiconductors, because the nature of semiconductors allow for a relatively high voltage which is easy to measure. It is also easily reproduced in a school or college Physics laboratory. So let's have a look at what happens.
The separation of charges leads to a potential difference, or voltage that is called the Hall voltage (V_{H}). This voltage also causes an electric field, E which is uniform. The idea is shown in the picture below:
We know that the electric field, E is given by:
We also know from the definition of electric field that the force is:
F = Eq
So we can write:
We also know that F = Bqv from Magnetism Tutorial 1, so we can write:
The q terms obligingly cancel out and we can rearrange to give:
Measuring the speed of individual electrons is not at all easy, but if we review , we know that:
I = nAvq Where:
So we rearrange to get:
and then substitute:
Now area, A = dt, so we can write:
and the d terms cancel out to give us our final relationship:
where:
The number of charge carriers per unit volume for typical semiconductors is shown in the table:
These figures are for a temperature of 300 K. The number of free charge carriers per unit volume rises as the temperature rises. We will use these, as college and university physics labs tend to have a temperature of about 300 K (27 ^{o}C). You would be well boiling if the temperature in the lab was 400 K.
For metals:
The Hall effect in theory can be observed in metals, but the Hall voltage would be so tiny that it's negligible. A calculation using the data above in a copper wire gives a Hall voltage of about 2 × 10^{9} V.
Uses of the Hall Effect In the school or college lab, the Hall probe is used to measure the value of a magnetic field. The picture shows two Hall probes:
The Hall probes are calibrated using a magnetic field of known flux density to reduce uncertainty.
Hall probe sensors are used in motor control to detect the speed of the motor. Hall probe sensors are used to detect wheels locking in antilock braking systems.
