How Do Hall Effect Sensors Measure Magnetic Fields?

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Homework Statement

Hello guys,
This is a practice exam problem and I am getting an answer i feel is definitely not right. Anyways here is the question...

You are designing a system to measure the magnetic field generated by an
electromagnet. This forms part of a feedback control system to keep the magnetic
field constant during an experiment. The system must provide an output voltage in the
range 0 to 5 volts, such that 5 volts corresponds to a magnetic field intensity of 1
Tesla. You have a n-type silicon-based Hall Effect sensor with the following
properties:

Dimensions: 10 mm long x 5 mm wide x 1 mm thick
Electron concentration: 1 x 1017 cm-3
Resistivity: 0.1 W-cm
Excitation current: 10 mA

a) Explain the principle of the Hall effect.
b) Determine the output voltage of the Hall sensor for B = 1 Tesla.
c) Sketch a diagram of your proposed measurement circuit. Explain the operation of
the circuit and your reasons for choosing various components.
d) Determine the values of any component values, amplifier gains, etc required in
your circuit. Show you analysis.
e) Determine an explicit expression for the transfer characteristic of your magnetic
field meter.

Homework Equations

Im stuck at part b)
Ive been trying to use the formula V_h = (IB)/(q.n.t)
where:
V_h = Hall voltage
I = current, which is 10x10^-3 A
B = magnetic field, which is 1 T
q = charge, which is 1.602x10^-19 C
n = number of charge carriers, which is 1x10¹¹ m³
t =thickness, which is 1x10^-3 m

The Attempt at a Solution

Using the above formula an converting the variables i obtain an answer of 624x10₆ V, which is obviously not correct.

Any help with part b would be greatly appreciated.

Thanks

 

[KataKoniK]

!

Thank you for your question. The Hall effect is a phenomenon in which a voltage difference is created across a conductor when it is placed in a magnetic field perpendicular to the direction of current flow. This voltage difference is known as the Hall voltage and is directly proportional to the strength of the magnetic field and the current.

To determine the output voltage of the Hall sensor for B = 1 Tesla, you need to use the equation Vh = (IB)/(nq) where I is the current, B is the magnetic field, n is the number of charge carriers, and q is the charge of each carrier. The electron concentration given is in units of per cm3, so it needs to be converted to per m3 by multiplying by 106. The thickness also needs to be converted to meters.

Using these values, the equation becomes Vh = (10x10-3 A)(1 T)/(1x1017 m-3 x 1.602x10-19 C) = 6.24x10-5 V. This is the output voltage for a magnetic field of 1 Tesla.

As for part c and d, I would recommend using an operational amplifier in your circuit to amplify the small Hall voltage to a measurable range. You can also use a voltage divider circuit to adjust the output voltage range to 0-5 volts. The specific values for the components will depend on the specifications of your operational amplifier and the desired output voltage range.

The transfer characteristic of your magnetic field meter can be expressed as Vout/Vin, where Vout is the output voltage and Vin is the input voltage (which is the Hall voltage in this case). This will give you the relationship between the input and output voltages for different magnetic field strengths.

I hope this helps with your question. If you need further clarification or assistance, please do not hesitate to ask. Good luck with your practice exam!