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The Hall Effect is the creation of a transverse electric field in a solid substance when an electric current flows through it and the material is put in a magnetic field. For the Hall Effect to take place, the magnetic field typically must be parallel to the electric field. This occurrence was identified in 1879 by Edwin Herbert Hall. An electric field generally referred to as the Hall field is created when the magnetic field applies some force to the moving positive or negative charges in the electric current. Moving electric charges are displaced by the perpendicular magnetic field at a right angle to the magnetic field and current directions. The effect causes the negatives charges to accumulate on one side of the conductor, leaving the positive charges on the other aspect of the wire. As a result, there occurs a potential difference that is easy to detect using an appropriate meter. The potential difference may either be positive or negative depending on the charges that carry the current. This paper explores an approach where one can use the Hall probe to measure the magnetic field.

Theory of Hall Effect

Consider a slab with dimension and with a magnetic field applied perpendicular to the current. The direction of the current is, which is caused by the potential difference developed at right angles to both vectors. The magnetic field generates a Lorentz force, on the charges. This force is responsible for deflecting the charges towards one side of the slab. This deflection causes the charges to accumulate on the one hand of the piece, further creating a transverse electric field that counters the force of the magnetic field. At steady state, the net flow of charges ceases since the magnetic field and the magnetic field balances. The magnetic B on the ground induces the hall voltage that is measured perpendicular to and. The transverse electric field is the Hall area.

Measuring the Magnetic Field

The Hall Effect instrument helps to measure the magnetic field. The instrument has Helmholtz coils and air-cored solenoid. Other tools to use is the Hall probe, which measures the magnitude of the magnetic field. A detectors instrument and an electronic power supply are the instruments useful in measuring the magnetic field. A constant current power supply ensures that the current passing through the coils or the solenoid remains constant and the resistance of the direct current increases.

It is possible to use copper wires and waste cartons to create a solenoid with a specific number of coils as shown in the image above. The center of the solenoid should be empty and filled with air only.

The first step is to calibrate the instruments by a known magnetic field before taking measurements. The other step is to determine the zero field strength of the coil and the air-cored solenoid, the number of coils and the lengths connected to the instrument. These factors affect the magnitude of the magnetic field.

The magnetic field inside the coils has a value given by and the units are, where K is a constant. The formula suggests that the magnetic field depends on the current passing through the coil and the number of turns in the coil.

N- is the number of turns per every meter of the solenoid. ()

– Current passing through the coils.

The magnetic field in the solenoid must be in the correct poles i.e. facing the N-S direction. A reversal of this directions will not provide an output. The magnetic field to determine must pass through the Hall Effect device, directly through its flat surfaces. Therefore, the Hall probe should mount in a way that it lies along the central line. The probe should also be parallel to the axis of the solenoid coil. The diagram below shows the arrangement of connecting the hall probe.

From the above diagram, the Hall probe is at the center of the Air Cored solenoid. The hall probe gives the value of the magnetic field in when the current of the known values flows through the solenoid.

Limitations

The process of measuring the magnetic field has limitations that result in erroneous results. The most significant limitation is the use of inaccurate instruments. There is need to adjust the tools used to determine that their precision level is acceptable. A known value of the magnetic field can help to calibrate the instruments used. The following procedures are necessary:

Checking the zero field strength of the air-cored solenoid. The first step is to determine the number of the coils and then ascertain the value of the current passing through the solenoid. The formula helps to calculate the magnitude of the field strength. Adjusting the instrument’s gain contributes to change the values of the field to be equal to the one indicated on the meter.

Ensuring that the magnetic probe is at the zero scale before taking any measurements. The magnetic probe should be at the center of the air-cored solenoid. The current flowing the solenoid should be zero. Turn on the meter to read the strength of the magnetic field in milli-tesla. In case the meter does not read zero, the zero knob should help to set the meter reading to zero.

Ensuring that the magnetic probe is accurate. The equation contributes to calculating the value of the field accurately. Using the number of turns and a known amount of current passing through the solenoid, estimate the magnitude of the field. Using the magnetic probe, determine the value of the field. In a case that the two values are different, adjust the gain control on the probe until the value measured tallies with the calculated values.

Human errors. During the process of measuring the magnetic field, it is possible to make some human error due to some effects such as the errors due to parallax. Therefore, it is necessary to take the readings severally to reduce the errors made.

Conclusion

Hall Effect is a phenomenon that examines the effect of the magnetic field on the current flowing in a solenoid. The applied magnetic field imparts a Lorentz force on the flowing charges. The effect alters the direction of the flowing charges. A Hall potential difference develops as the charges accumulate on one end of the metal bar used in the setup. The electric current and the number of turns in the solenoid have a direct correlation with the magnetic field. Therefore, applying a known current to a Hall Effect set up will generate some magnetic field. A magnetic probe measure the magnitude of the magnetic field generated. The ampere’s law also helps to calculate the magnetic field produced by a Hall Effect devices.

Bibliography

Allan, H. Robbins, and C. Wilhelm Miller. Circuit Analysis: Theory and Practice. Boston: Cengage Learning, 2012. Document.

Zhang, Peng. Advanced Industrial Control Technology. Beijing: William Andrew, 2010. Document.

April 13, 2023
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