‘The Hall Effect' as it is known, was discovered almost accidentally by Edwin Herbert Hall, an American physicist, at the age of 24 in 1879, as he was working on his doctoral thesis for university under the supervision of Henry Augustus Rowland. 
Interestingly, Edwin Hall's discovery predated the discovery of electrons by almost twenty years. Electrons, however, are vital in the modern explanation of the Hall Effect theory to explain the creation of electronic fields. At the time of discovery, electric current was not believed to be a group of separate particles, but widely believed to be a single mass of continuous fluid. 
Without the knowledge of electrons as an aid, Hall's discovery came from initial research carried out in the 1820's by Andre Ampere, the French mathematician who founded the science of Electromagnetism and whose name was given to the measure of electric current. . Ampere discovered that mechanical forces became apparent on current carrying wires when they were placed into a magnetic field. What Edwin Hall did, was question whether the mechanical force was acting upon the wires themselves or the currents within the wires. Hall replaced the simple wire which was affected by the magnetic field with a thin rectangle of gold through which current was flowing, and was able to determine that if the force from the magnetic field was acting on the current flowing through the plate, the current would be forced to congregate on one side. In addition to the production of a force, a small voltage would also be created by the crowding of the current on one side of the plate. 
Quite early on after its discovery, the Hall Effect became a commonly used principal for physicists. From as early as the 1920's it is documented in textbooks where it has been tested using a number of different materials. However it wasn't until the mid 20th Century that the Hall Effect was used to create transducers that became commonly used in laboratory equipment and eventually was adapted for and used on integrated circuits in which the principle remains the same to this day. These integrated circuits are used in countless applications in modern life. 
Principles of the Hall Effect
Figures two and three are a representation of the basic principles of Hall Effect devices. They illustrate current flowing through a thin sample of semi conducting material known as the hall element. Connected to this sample of material, perpendicular to the flow of the current, are two output connections that will measure the voltage produced when the magnetic field is activated.
In Figure 2 there is no magnetic field acting on the Hall element. The flow of current through the material is uniform and unchanged and zero perpendicular voltage or potential difference is created as a result. 
In Figure 3 a magnetic field has been introduced to the Hall Element. As it can be seen, the force from the magnetic field has disturbed and distorted the electrical current. The force has caused the charge carriers flowing through the Hall Element to crowd along its top side. This creates a negative charge on the side of the Hall Element with the crowding charge carriers and a positive charge on the clearer side. This in turn causes a measurable potential difference to form across the width of the Hall Element which can be measured using the outputs. The voltage created by this distortion is known as the ‘Hall Voltage' . .The potential difference created in the Hall Element is proportional to the flux (B), current (I) and resultant charge separation present in it . The relationship between the magnetic field's flux density (B) and the current (I) can be observed using the equation  :
The flux density (B) referred to in this equation translates as the amount of magnetism that is induced into the Hall Element by the mechanical force. 
The value of voltage generated due to the Hall Effect can be calculated using the equation:
Where refers to the hall effect constant, which is described as a factor of the number of electrons per unit volume and the electron charge, and is measured using the units z is the thickness of the conductor being used. 
In the previous description the Hall Element has always been a sample of semiconducting material such as silicon. These materials are used as their properties are far more useful when being used to produce the Hall Effect than extremely conductive metal materials or non-conductive material.
In Highly conductive materials there is an extremely high carrier density, which refers to the volume density of mobile charge carriers in a material. In the case of metals these charge carriers are electrons. Once the carrier density has been obtained in a material, the speed at which the charge carriers move (drift velocity) can be calculated based on the current. In a conductive material such as a metal, this drift velocity tends to be very low. Even with a strong magnetic field, this results in an extremely small resultant voltage due to the Hall Effect.
To this end, it was determined that the way to increase the voltage that the Hall Effect produced was to find a material with a lower carrier density than metals. A material such as this would display the Hall Effect with greater effect for a metal with a similar current being passed through it. Semiconducting materials were determined as the best materials to carry out this task. They have a much lower carrier density than metals, which, using the equation :
Allows the determination that the drift velocity will be higher, therefore increasing the resulting Hall Voltage () when the following equation is used:
Development of Hall Effect Devices
The earliest usage of Hall Effect transducers were in physics laboratories in the 1950's, they were widely used in magnetic measuring equipment. They were preferred because of the high availability of semiconductor materials. In the 1960's and 1970's, advances in technology meant that Hall Effect sensors could be built into integrated circuits. This, coupled with the fact that these sensors caused a vast reduction in the costs of using the devices they were placed in, meant they could start being produced for widespread practical uses. One of the earliest major uses for these sensors was in computer keyboards. The addition of the Hall Effect sensors into these systems meant mechanical solid state contacts were replaced by electro mechanical contacts. This greatly improved the reliability and durability of the keyboards as mechanical switches were prone to wear and failure. Developments have continued to progress, and in our current technological state, Hall Effect sensors play a major roll in many everyday devices. The most common applications being speed, current, proximity and position. But these applications are used many times for various products in industry. 
Advantages and Disadvantages
Although Hall effect sensors are by no means the most accurate way of measuring magnetic fields their advantages far outweigh their drawbacks:
- Durability Hall Effect Sensors have been tested in extremely hostile environments and have proved that they are extremely versatile and resistant to moisture, dust and other contamination. Certain models are capable of withstanding temperatures from -40C to 150C, and they are also extremely resilient to shock and vibration due to the fact that they are constructed as monolithic integrated circuits, in which the base plate of the microchip contains many of the active components that are involved in the operation of the circuit board. Hall Effect sensors are far more durable than sensors with mechanical contacts which are prone to wearing. [1 & 5]
- Cost Effectiveness As stated, Hall Effect transducers are not the most accurate device in carrying out their task, however this is reflected in their price. Despite the fact that the most complex, top of the range models of Hall Effect Transducers can cost substantial amounts of money, most can be purchased for minimal cost. Their design means there are no undesired influences on the system that cause its results to deviate slightly and that need to be countered for. This is due to the surface elements of the component, and causes Hall Effect Transducers to be highly reliable and simple to reproduce. 
- Size Hall Effect transducers can currently be made on an almost microscopic scale, meaning they can be fitted to circuit boards and can be used places where any other form of magnetic transducer would simply be too large and impractical to place.
Hall Effect Proximity Sensors
Without the aid of a magnet with a strong field, a Hall Effect Sensor normally only has an effective range of approximately 10cm , but with a powerful magnet this distance can be increased relative to the size of the magnetic field that the magnet produces and to the size of the Hall Effect sensor. To this end, a Hall Effect Sensor can be effectively used as a proximity sensor for use in various applications, both short and to a lesser extent, long range.
The way in which these work is simple, a Hall Effect sensor with a magnetic field already present (due to a permanent magnet) on the Hall Element is activated. This would result in a potential difference value being created on the perpendicular outputs that can be monitored. As an object enters the magnetic field of the sensor it becomes distorted. This would disrupt the flow of particles in the Hall Element and would thus cause a slight change in the potential difference measured on the perpendicular outputs. As the object moves closer to the Hall Effect Sensor, the magnetic field would become increasingly distorted and the potential difference on the outputs would continue to change. Once the potential difference reached a certain value, a switch would be triggered that would indicate that the object is a certain distance from the sensor and further action is then taken.
Applications for this type of Hall Effect sensor include machinery in which contaminants such as dirt or dust are common or vibration occurs. They are also used where the sensor is required to be submerged in water. In situations such as this, Hall Effect sensors are much more useful than optical or light sensors which have a similar purpose. An example of applications such as this are in automotive components.
Hall Effect Flow Rate Sensors
Flow Rate Sensors can be made using Hall Effect sensors in multiple ways however the general principal remains largely similar. Each activation of the sensor, due to an interruption of a magnetic field and a resulting change in the potential difference being recorded from the Hall Effect device, corresponds to a certain quantity of water passing the sensor.
One example in which a sensor such as this is used, as demonstrated in figure 4, is when two magnets are placed at 90 to each other on a plate which rotates when it is subjected to water trying to force its way past. There is a Hall Effect Sensor on one side of this plate, and as it spins the magnetic fields of the two magnets activate the sensor. A certain amount of activations of this sensor corresponds to a certain amount of liquid being passed through it. 
The advances in recent technology has allowed the medical profession to make use of Edwin Halls discovery to create a Flow Rate Sensor that allows doctors to measure a patients blood flow. This is done by utilizing the fact that the velocity of the charged particles that are flowing through a conductor is directly related to the amount of voltage produced by using the Hall Effect. A persons blood flow can be measured in this way by placed two small voltage probes on either side of the blood vessel. Two opposing magnetic poles are then held on either side of the blood vessel perpendicular to the way in which the voltage probes were placed. The resulting voltage generated due to the potential difference of the hall effect directly relates to an indication of a persons blood flow.
In conclusion, Hall Effect sensors are used for a vast multitude of uses in society today, ranging from the automotive industry and industrial machines to the medical profession and mobile phones. Edwin Halls accidental discovery has aided in quite a dramatic jump in technology over recent years due to cost effective and dimensional advantages of the devices that the Hall Effect has helped to develop.
- Edward Ramsden, “Hall Effect Sensors” E-Book. Retrieved: 26/11/09
- Encyclopedia Britannica (2009). “Andr-Marie Ampre.” Retrieved: 1/12/09 from Encyclopedia Britannica Online: http://www.britannica.com/EBchecked/topic/21416/Andre-Marie-Ampere
- Edward Ramsden, “Hall Effect Sensors” E-Book. Retrived: 26/11/09
Chapter 1 Hall Effect Physics
Electronic Location: http://wobl.engineeringvillage.com/wobl/9780750679343/9780750679343.pdf?expires=1259502814117&ticket=7bf505f7d29a7fd3c2c6d29ec809c43f&custid=993755&EISESSION=1_18e85411252c029c862937ses2
- Honeywell Inc. “Hall Effect Sensors Chapter 2”. Retrieved: 26/11/09 http://content.honeywell.com/sensing/prodinfo/solidstate/technical/chapter2.pdf
- “Hall Effect Sensors and Magnetoresistance”. Retrieved: 26/11/09. http://academic.udayton.edu/markpatterson/ECT459/HallEffect.pdf
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- Considine, Process/Industrial Instruments and Controls Handbook, McGraw Hill, 1993,pages 5.67
- Areny, Sensors & Signal Conditioning, John Wiley & Sons, 1991, pages 67-8
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- “Magnetic Flux Density”. Retrieved: 30/11/09 http://www.tompotter.us/b.html
- Wayne Storr. (2009) “Magnetic Hall Effect Sensor” Retrieved: 1/12/09 http://www.electronics-tutorials.ws/electromagnetism/hall-effect.html
- Honeywell Inc. “Honeywell Hall Effect Sensing and Application”. Retrieved: 26/11/09 http://content.honeywell.com/sensing/prodinfo/solidstate/technical/hallbook.pdf
- Soylent Communications(2009). “Edwin Hall”. Retrieved: 2/12/09 http://www.nndb.com/people/130/000099830/