# To calibrate an uncalibrated Hall probe and use it to investigate how the magnetic flux density mid-way between opposite poles of two permanent bar magnets varies with the separation of the bar magnets.

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Introduction

Physics Practical Examination 2 (Part A – Planning Exercise)

The aim of this experiment is to calibrate an uncalibrated Hall probe and use it to investigate how the magnetic flux density mid-way between opposite poles of two permanent bar magnets varies with the separation of the bar magnets.

To initially calibrate the Hall probe, a solenoid will be used to create a uniform magnetic field and the Hall probe will be placed in the centre of the solenoid.

The magnetic flux density at this point can be calculated using an equation:

B = μ0 N I ^{[1]}

where B is the magnetic flux density, μ0 is the permeability of free space, N

is the number of coils per metre and I is the current applied to the solenoid.

At a number of different applied currents (five or more readings), along with calculating the magnetic flux density the Hall voltage should also be noted (a voltage induced in the Hall wafer). The potential difference created is known as the Hall effect ^{[2]}.

Middle

v is the speed at which the electrons move

Once the electrons move and create a potential difference across the opposite sides of the semiconductor wafer, the force created by the magnetic filed is opposed by an electric force due to the Hall voltage. This can be calculated using the equation:

Felectric = Q VH

d

where Q is the charge on the electron, VH is the Hall voltage and d

is the distance between the two opposite sides of the semiconductor wafer

Combining these two equations gives another equation:

B Q v = Q VH

d

Simplifying this equation gives:

VH = B v d

As long as the current is kept constant, v and d are both constants therefore VH is proportional to B.

To ensure the data obtained are accurate, the Hall probe should be kept parallel to the Earth’s magnetic field to ensure that it has no effect. Also the temperature needs to be kept constant to ensure that the charge carriers in the Hall probe move at a constant velocity.

Conclusion

The magnets should not be mounted using iron clamps, as iron has a high permeability and is magnetic, so would draw flux into it; thereby affecting the results obtained ^{[4]}. To cater for the Earth’s magnetic field, the Hall probe can first be used outside of the field of the two bar magnets so that the Earth’s magnetic field can be measured; this result can then be subtracted from each subsequent result obtained to measure the true magnetic flux density of the bar magnets.

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[1] http://www.physics.carleton.ca/~watson/1000_level/Magnetism/1004_Magnetic_field.html

[2] http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html

[3] http://www.physics.gatech.edu/advancedlab/labs/hall/hall-2.html

[4] http://www.aacg.bham.ac.uk/magnetic_materials/soft_magnets.htm

This student written piece of work is one of many that can be found in our AS and A Level Fields & Forces section.

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