Hall effect sensing principle

1. Introduction
   
   Hall effect is one of the the sensing elements that has been used in the design of many different sensors. I find this type of sensing interesting, and therefore, in this wiki page I will discuss briefly the physical principle of sensing based on Hall effect.

   The Hall effect was discovered in 1879 by Dr. Edwin Herbert Hall while he was at Johns Hopkins University in Baltimore. While trying to verify electron flow theory proposed by Kelvin, he found that when a magnet was placed with its fields being perpendicular to one face of a thin rectangle of gold which current was flowing through, a potential difference appeared at the opposite edges. What he found is that this voltage is proportional to the current flowing through the conductor, and the flux density or magnetic induction perpendicular to the conductor. He experiments were successful and well received at the time. [1]

2. Theory of the Hall effect
   
   The Hall effect is based on the interaction between moving electric carriers and an external magnetic field. If an electric current flows through a conductor in an external magnetic field, then a transverse force call Lorentz force caused by the magnetic field will exert on the moving charge carriers, which pushes these carriers to one side of the conductor. A buildup of charges at the sides of the conductors will balance this magnetic influence, producing a measure voltage between the two sides of the conductor. The presence of this voltage is called the Hall effect, and this voltage is the Hall voltage. [3,103-105]
   
   
                                                                                Figure 1. Hall effect principle with magnetic field present [2]
   
   Figure 1 shows the principle of Hall effect with the direction of current being the conventional current. The magnetic field is perpendicular to both the direction of the current and the Lorentz force. The magnetic forceis given by

   

   whereis an electronic charge, is the speed of an electron, and is the magnetic field. If the Hall voltage is, and the width of the conductor is, then the magnitude of the electric field is given by

   

   Now the electric force on a charge is

   

   The electric force acts in opposition to the magnetic force. In a steady state, the two forces are equal

   

   Suppose the thickness of the conductor in figure 1 is, the length of the conductor is and that it containsmobile charge carriers per unit volume. It follows that the total current flowing through the conductor can be written as

   

   Because all mobile charges contained in a rectangular volume of length, width, and thickness, flow past a given point in the conductor in one second. Combining equations (1) and (2) yields

   

   From equation (3), we come to a conclusion that Hall voltage is proportional to the current flowing through the conductor, and the magnetic field strength, and is inversely proportional to the number density of mobile charges and the thickness of the conductor. This has important meanings in practice. In order to build a sensitive Hall probe, we need to take a thin conductor of some material which possesses very few mobile charges per unit volume (e.g, semiconductor), and then run large current through it.
   Another important point worthing pointing out is that very often the angle between the magnetic field vector and the current vector is not always perpendicular. At a fixed temperature the Hall voltage is given by

   
3. Hall effect accelerometers
   
   Until now the physical principle of Hall effect sensing element has been studied. This section will try to find out how this sensing element is used in Hall effect sensor. Four questions will be answered to explain how it is applied. The following shows the US1881 Hall effect sensor to give a feel how it looks like.
                                                                                                   Figure 2. US1881 Hall effect sensor [3]
   
   The first question is if the Hall effect sensors convert the stimulus directly into electrical output

Add a new wiki page under the Physical principles of sensing and write about the physics behind the scene. You may try to find answers to the following questions:

• Does your sensor convert the stimulus directly into electric output?
• What steps are required to transform the signal into electric output?
• What types of physical effects and energies are involved in the sensing and in transformation?
• How the sensing and transformation can be modeled mathematically or physically?

After completing all this, click the Submission button below and write shortly:

• What have you done so far on this course?
• How much time have you spent?
• What have you learnt so far?
• What has been most difficult for you?

References

1. Bridgemen, P. W. (1939). Biographical Memoir of Edwin Herbert Hall. National Academy of Sciences.
2. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html
3. https://www.sparkfun.com/products/9312
4. Jacob Fraden. Handbook of Modern Sensors: Physics, Designs, and Applications (4th edition). Springer Publishing
5. http://farside.ph.utexas.edu/teaching/302l/lectures/node74.html
6. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html
7. http://sensing.honeywell.com/honeywell-sensing-sensors-magnetoresistive-hall-effect-applications-005715-2-en.pdf