Hall Effect and Applications

What Is the Hall Effect?

The Hall Effect occurs when a current-carrying conductor or semiconductor is placed in a magnetic field perpendicular to the current.

The moving charge carriers experience a magnetic force. They are pushed toward one side of the material, producing a separation of charge.

This creates a voltage across the material called the:

Hall voltage, V_H

The Hall Effect therefore provides a direct connection between:

moving charge + magnetic field → charge separation → measurable voltage

It is widely used to measure magnetic fields and detect position, motion, speed and electric current.

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The Basic Hall Effect Setup

Consider a thin rectangular conducting or semiconducting strip.

A current flows along its length.

Now place the strip in a magnetic field perpendicular to the current.

For example:

• current → to the right
• magnetic field → into the page
• magnetic force → toward one side of the strip

Charge carriers accumulate along one side.

The opposite side is left with the opposite net charge.

A potential difference develops across the width.

This is the:

Hall voltage

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Why Moving Charges Are Deflected

A moving charged particle in a magnetic field experiences:

F_B = |q|vB sin θ

where:

• F_B = magnetic force
• |q| = charge magnitude
• v = charge-carrier drift speed
• B = magnetic flux density
• θ = angle between v and B

If the motion is perpendicular to the magnetic field:

θ = 90°

so:

F_B = |q|vB

The force is perpendicular to both the motion and magnetic field.

This pushes charge carriers sideways.

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Direction of Magnetic Force

For a positive charge, the magnetic-force direction can be found from:

F = q(v × B)

A right-hand rule can determine the direction.

For negative charge carriers such as electrons, the force direction is opposite to that for a positive charge moving in the same direction.

This is important because Hall measurements can provide information about the type of charge carriers present in a material.

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Charge Separation

As charge carriers move sideways, they accumulate on one side of the material.

This creates:

• excess charge on one side
• opposite net charge on the other side

The separated charges create an internal electric field across the material.

This field is called the:

Hall field

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The Hall Electric Field

As more charge accumulates, the Hall electric field becomes stronger.

The electric force on a charge is:

F_E = |q|E_H

where E_H is the Hall electric-field strength.

The electric force acts opposite to the sideways magnetic deflection.

Eventually:

electric force = magnetic force

At this point, charge carriers no longer continue accumulating significantly on one side.

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Force Balance

At equilibrium:

F_E = F_B

Therefore:

|q|E_H = |q|v_dB

where v_d is the drift speed.

Cancel |q|:

E_H = v_dB

This relationship explains how the Hall electric field depends on:

• charge-carrier drift speed
• magnetic flux density

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From Hall Field to Hall Voltage

If the width across which the Hall voltage is measured is w:

V_H = E_Hw

Since:

E_H = v_dB

then:

V_H = v_dBw

This shows that a stronger magnetic field produces a larger Hall voltage when other quantities remain constant.

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Current and Charge-Carrier Density

Electric current in a conductor can be related to charge-carrier motion by:

I = nqAv_d

where:

• I = current (A)
• n = number of charge carriers per unit volume (m⁻³)
• q = charge per carrier (C)
• A = cross-sectional area (m²)
• v_d = drift speed (m/s)

For a Hall sample with width w and thickness t:

A = wt

Therefore:

I = nqwtv_d

Rearranging:

v_d = I/(nqwt)

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Hall Voltage Equation

Starting with:

V_H = v_dBw

and substituting:

v_d = I/(nqwt)

gives:

V_H = [I/(nqwt)]Bw

The width cancels:

V_H = IB/(nqt)

For magnitude:

|V_H| = IB/(n|q|t)

where:

• V_H = Hall voltage (V)
• I = current (A)
• B = magnetic flux density (T)
• n = charge-carrier number density (m⁻³)
• q = charge per carrier (C)
• t = thickness of the Hall element (m)

This is an important Hall Effect relationship.

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Factors Affecting Hall Voltage

From:

|V_H| = IB/(n|q|t)

we can identify several important relationships.

Current

V_H ∝ I

Larger current → larger Hall voltage.

Magnetic flux density

V_H ∝ B

Stronger magnetic field → larger Hall voltage.

Charge-carrier density

V_H ∝ 1/n

Lower carrier density → larger Hall voltage.

Thickness

V_H ∝ 1/t

Thinner Hall element → larger Hall voltage.

Charge per carrier

Larger |q| reduces Hall voltage for the same carrier density and other conditions.

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Why Semiconductors Are Useful

Hall Effect devices are often made using semiconductors rather than ordinary metals.

Semiconductors can have much lower charge-carrier densities than metals.

Since:

V_H ∝ 1/n

a lower carrier density can produce a larger and easier-to-measure Hall voltage.

This makes semiconductors particularly useful for Hall sensors.

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Example: Effect of Magnetic Field

A Hall sensor produces:

V_H = 20 mV

in a magnetic field:

B = 0.10 T

The field is increased to:

B = 0.30 T

Since:

V_H ∝ B

the field has tripled.

Therefore:

V_H = 3(20)

V_H = 60 mV

provided the other quantities remain constant.

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Example: Effect of Current

A Hall element produces:

V_H = 5.0 mV

when:

I = 10 mA

The current is increased to:

20 mA.

Since:

V_H ∝ I

doubling current doubles the Hall voltage:

V_H = 10 mV

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Example: Effect of Thickness

Two Hall elements are identical except for thickness.

Sensor A:

t = 1.0 mm

Sensor B:

t = 0.50 mm

Since:

V_H ∝ 1/t

Sensor B is half as thick.

Therefore, under the same conditions:

Sensor B produces twice the Hall voltage.

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Example: Calculating Hall Voltage

Suppose:

I = 0.020 A

B = 0.50 T

n = 5.0 × 10²² m⁻³

|q| = 1.60 × 10⁻¹⁹ C

t = 1.0 × 10⁻³ m

Use:

V_H = IB/(n|q|t)

V_H = (0.020)(0.50) / [(5.0 × 10²²)(1.60 × 10⁻¹⁹)(1.0 × 10⁻³)]

The denominator is:

8.0

Therefore:

V_H = 0.010/8.0

V_H = 1.25 × 10⁻³ V

V_H = 1.25 mV

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Hall Coefficient

Another useful quantity is the:

Hall coefficient, R_H

For a simple material with one dominant charge-carrier type:

R_H = 1/(nq)

The sign of R_H depends on the sign of the dominant charge carrier.

The Hall voltage can then be written:

V_H = R_HIB/t

The Hall coefficient can therefore provide information about:

• carrier concentration
• carrier type

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Identifying Charge Carriers

One historically important use of the Hall Effect is determining whether the dominant charge carriers behave as:

• negative carriers
• positive carriers

The polarity of the Hall voltage depends on the charge-carrier sign.

In many metals, the dominant mobile carriers are electrons.

In semiconductors, conduction can be dominated by:

• electrons
• holes

Hall measurements are therefore valuable in semiconductor physics.

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What Is a Hall Probe?

A Hall probe is a device that uses the Hall Effect to measure magnetic flux density.

A Hall probe contains a small Hall element carrying a known current.

When placed in a magnetic field:

magnetic field → Hall voltage

The instrument measures this voltage and converts it into a value of:

B

usually measured in:

• teslas (T)
• milliteslas (mT)
• microteslas (μT)

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How a Hall Probe Measures Magnetic Fields

The process can be summarized:

1. A known current passes through the Hall element.
2. The probe is placed in the magnetic field.
3. Moving charge carriers experience magnetic force.
4. Charge separation occurs.
5. A Hall voltage develops.
6. The voltage is measured.
7. Calibration converts voltage into magnetic flux density.

Therefore:

Hall voltage → measurement of B

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Probe Orientation

Hall voltage depends on the component of magnetic field perpendicular to the current-carrying Hall element.

If the relevant angle is θ:

V_H ∝ B sin θ

Maximum response occurs when:

θ = 90°

If the magnetic field is oriented so that the relevant perpendicular component is zero:

Hall voltage ≈ 0

Correct probe orientation is therefore essential when measuring magnetic fields.

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Finding Magnetic-Field Direction

A Hall probe can also help determine magnetic-field direction.

Changing the direction of B reverses the direction of magnetic force on the charge carriers.

Therefore, the polarity of the Hall voltage reverses.

A properly designed instrument can use this to distinguish:

+B from −B

along its measurement axis.

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Mapping Magnetic Fields

Hall probes can measure the magnetic field at many different positions.

For example, a student could move a Hall probe around:

• a bar magnet
• a solenoid
• an electromagnet

and record B at each location.

This allows the field to be mapped quantitatively.

Unlike iron filings, a Hall probe provides numerical measurements of magnetic flux density.

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Example: Solenoid Investigation

Suppose a Hall probe is placed at the centre of a solenoid.

Current through the solenoid is gradually increased.

For an ideal long solenoid:

B = μ₀nI

Therefore, increasing I increases B.

The Hall probe detects this because:

B ↑ → V_H ↑

This experiment can be used to investigate the relationship between:

solenoid current and magnetic flux density

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Hall Effect Sensors

A Hall Effect sensor uses the Hall Effect to detect a magnetic field.

Modern Hall sensors often contain:

• Hall element
• amplifier
• signal-processing electronics
• switching or digital circuitry

A very small Hall voltage can therefore be amplified and converted into a useful electrical output.

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Analogue Hall Sensors

An analogue Hall sensor can produce an output that varies continuously with magnetic-field strength.

For example:

weak field → small output

stronger field → larger output

These sensors are useful when the system needs to measure:

how strong the magnetic field is

rather than simply detecting whether a magnet is present.

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Digital Hall Sensors

A digital Hall sensor can operate like an electronic switch.

For example:

magnet far away → OFF

magnet approaches → ON

The Hall element detects the field, while internal electronics determine whether the field exceeds a particular threshold.

This is useful for:

• position detection
• limit switches
• door sensors
• speed measurement

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Detecting Position

A magnet can be attached to a moving object.

A stationary Hall sensor detects when the magnet approaches.

Therefore, the sensor can determine whether an object has reached a particular position.

Applications include:

• robotic mechanisms
• industrial machinery
• vehicle systems
• electronic controls
• automatic doors

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Detecting Rotational Speed

Hall sensors can measure rotational speed.

A small magnet is attached to a rotating wheel or shaft.

Each time the magnet passes the Hall sensor, the sensor produces a pulse.

If the sensor detects:

N pulses per second

and there is one magnet on the wheel:

rotation frequency = N rotations per second

If there are multiple magnets, the number of pulses per revolution must be considered.

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Example: Rotational Speed

A wheel contains one magnet.

A Hall sensor detects:

20 pulses per second.

Therefore:

f = 20 revolutions/s

To convert to revolutions per minute:

rpm = 20 × 60

rpm = 1200

If the wheel had two equally spaced magnets, 20 pulses/s would correspond to only:

10 revolutions/s

or:

600 rpm

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Measuring Wheel Speed

Hall sensors can be used to monitor rotating wheels.

If wheel radius is known, rotational information can be converted into linear speed.

For a wheel:

v = 2πrf

where:

• v = linear speed
• r = wheel radius
• f = rotation frequency

This principle is useful in:

• bicycles
• vehicles
• industrial machinery
• robotics

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Brushless DC Motors

Hall Effect sensors are commonly used in some brushless DC motors.

The sensor detects the position of the rotor magnets.

The motor controller uses this information to determine when to switch current through different coils.

The sequence is:

rotor moves

↓

Hall sensor detects magnetic position

↓

controller determines rotor position

↓

current switches to appropriate winding

↓

electromagnetic torque continues

Hall sensors therefore help replace the mechanical commutator used in traditional brushed DC motors.

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Current Sensors

Hall Effect sensors can also measure electric current without requiring the sensor electronics to be directly in the main current path.

A current-carrying wire produces a magnetic field.

For a long straight wire:

B = μ₀I/(2πr)

Therefore:

current → magnetic field → Hall voltage

A Hall sensor measures the magnetic field and the system determines the current.

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Advantages of Hall Current Sensors

Hall-based current measurement can provide:

• electrical isolation
• measurement of large currents
• low interference with the main circuit
• measurement of DC as well as changing currents
• improved safety in high-power systems

These sensors are common in:

• electric vehicles
• battery systems
• power supplies
• industrial electronics
• renewable-energy systems

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Contactless Switching

Because Hall sensors respond to magnetic fields, they do not require direct mechanical contact with the moving object.

This allows:

contactless sensing

Advantages can include:

• reduced mechanical wear
• long operating life
• sealed operation
• high reliability
• operation in dusty or dirty environments

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Door and Lid Sensors

A magnet can be mounted on a door or lid and a Hall sensor on the frame.

Door closed:

magnet near sensor

Door open:

magnet moves away

The electronic system detects the change.

This can be used in:

• appliances
• laptops
• security systems
• industrial equipment

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Smartphones and Portable Electronics

Hall sensors can be used in portable electronics to detect nearby magnets.

For example, a device may detect:

• magnetic covers
• accessories
• opening or closing mechanisms

The sensor can then trigger a software or hardware response.

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Automotive Applications

Vehicles use Hall Effect sensors extensively.

Applications can include detecting:

• wheel rotation
• crankshaft position
• camshaft position
• motor position
• pedal position
• steering position
• current in electrical systems

Because Hall sensors can operate without direct mechanical contact, they are well suited to many vehicle systems.

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Robotics

Robots often need information about the position of moving components.

Hall sensors can detect magnets attached to:

• joints
• wheels
• motors
• grippers
• linear mechanisms

The resulting electrical signal can be sent to a controller.

The controller can then adjust motor operation.

This creates a:

feedback system

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Industrial Automation

Hall sensors can monitor:

• machine position
• shaft speed
• motor operation
• current
• magnetic-field strength

Because the sensing can be contactless, Hall sensors are useful in automated machinery where mechanical switches might wear out.

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Hall Effect vs Mechanical Switch

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Hall Effect vs Reed Switch

A reed switch can also respond to a magnetic field.

However, a traditional reed switch contains mechanical contacts that physically move.

A Hall sensor is electronic and has no comparable mechanical switching contacts.

Hall sensors are therefore useful when:

• rapid switching
• long lifetime
• electronic integration
• precise sensing

are important.

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Measuring Magnetic Field Strength

Suppose a Hall probe has been calibrated so that:

10 mV corresponds to 0.20 T.

If the relationship is linear, then:

20 mV corresponds to:

0.40 T

and:

5 mV corresponds to:

0.10 T

This illustrates how a Hall probe converts a small voltage into a magnetic-field measurement.

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Example: Finding B from Hall Voltage

Suppose:

V_H = 2.0 × 10⁻³ V

I = 0.040 A

n = 2.5 × 10²² m⁻³

|q| = 1.60 × 10⁻¹⁹ C

t = 5.0 × 10⁻⁴ m

Starting with:

V_H = IB/(n|q|t)

Rearrange:

B = V_Hn|q|t/I

Substitute:

B = [(2.0 × 10⁻³)(2.5 × 10²²)(1.60 × 10⁻¹⁹)(5.0 × 10⁻⁴)]/(0.040)

This gives:

B = 0.10 T

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Example: Finding Carrier Density

Suppose:

V_H = 4.0 × 10⁻³ V

I = 0.020 A

B = 0.40 T

t = 5.0 × 10⁻⁴ m

|q| = 1.60 × 10⁻¹⁹ C

Use:

V_H = IB/(n|q|t)

Rearrange:

n = IB/(V_H|q|t)

Substituting the values gives:

n = 2.5 × 10²² m⁻³

This shows how Hall measurements can be used to investigate the microscopic properties of materials.

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Designing a Sensitive Hall Sensor

From:

V_H = IB/(n|q|t)

a larger Hall voltage can be produced by:

• increasing current I
• increasing magnetic field B
• using a material with lower carrier density n
• decreasing Hall-element thickness t

However, engineering constraints matter.

Increasing current too much may cause:

heating

Making the sensor extremely thin may reduce:

mechanical strength

Choosing a material therefore involves balancing sensitivity with reliability.

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Limitations and Measurement Errors

Hall measurements can be affected by:

• incorrect probe orientation
• temperature changes
• electrical noise
• imperfect calibration
• nearby magnetic fields
• sensor offset
• limited sensor range

A good measurement procedure should therefore include:

• calibration
• correct alignment
• repeated measurements
• appropriate range selection
• control of nearby magnetic sources

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Common Mistakes

Mistake: Saying the Hall Effect occurs because charges are attracted to a magnet.
The sideways separation is caused by magnetic force on moving charge carriers.

Mistake: Saying a magnetic field creates the current.
In the basic Hall setup, a current is already flowing. The magnetic field deflects its charge carriers.

Mistake: Saying the Hall voltage develops along the same direction as the current.
The Hall voltage develops across the conductor, transverse to the current.

Mistake: Forgetting that magnetic force depends on particle motion.
Stationary charges do not experience magnetic force.

Mistake: Assuming charge continues accumulating indefinitely.
The growing Hall electric field eventually balances the magnetic force.

Mistake: Saying stronger B produces smaller Hall voltage.
For fixed conditions, V_H ∝ B.

Mistake: Saying thicker Hall elements produce larger Hall voltage.
For the standard geometry, V_H ∝ 1/t.

Mistake: Ignoring probe orientation.
A Hall probe responds to the appropriate component of the magnetic field.

Mistake: Assuming Hall sensors can only measure magnetic fields.
They can also be used for position, speed, current and proximity sensing.

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Key Terms

Hall Effect — production of a transverse voltage when moving charge carriers in a conductor or semiconductor are deflected by a magnetic field.

Hall voltage (V_H) — potential difference produced across a Hall element by charge separation.

Hall field (E_H) — electric field created across the material by separated charges.

Charge carrier — mobile charged particle responsible for electric current, such as an electron or hole.

Drift velocity (v_d) — average directed velocity of charge carriers due to an applied electric field.

Carrier density — number of mobile charge carriers per unit volume.

Hall coefficient (R_H) — material quantity related to carrier density and charge, with R_H = 1/(nq) for a simple one-carrier model.

Hall probe — instrument using the Hall Effect to measure magnetic flux density.

Hall sensor — electronic device using Hall voltage to detect magnetic fields.

Analogue Hall sensor — Hall sensor producing an output related continuously to magnetic-field strength.

Digital Hall sensor — Hall sensor producing switching or digital output when specified magnetic conditions are reached.

Contactless sensing — detecting position or motion without direct mechanical contact.

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Key Takeaways

• The Hall Effect occurs when moving charge carriers are deflected by a magnetic field.
• The magnetic force causes charge to accumulate on opposite sides of a conductor or semiconductor.
• This charge separation produces a Hall voltage.
• The growing Hall electric force eventually balances the magnetic force.
• For perpendicular motion, F_B = |q|vB.
• At equilibrium, E_H = v_dB.
• A useful Hall-voltage relationship is V_H = IB/(nqt), with sign depending on carrier type and geometry.
• Hall voltage increases with current.
• Hall voltage increases with magnetic flux density.
• Hall voltage increases as carrier density decreases.
• Hall voltage increases as Hall-element thickness decreases.
• Semiconductors are particularly useful for Hall sensors because their carrier densities can be relatively low.
• Hall measurements can provide information about charge-carrier type and density.
• A Hall probe converts Hall voltage into a measurement of magnetic flux density.
• Correct probe orientation is important.
• Reversing the magnetic field reverses Hall-voltage polarity.
• Hall sensors can detect position and proximity.
• Hall sensors can measure rotational speed.
• Hall sensors can help control brushless motors.
• Hall sensors can measure electric current indirectly by detecting the magnetic field produced by the current.
• Hall Effect technology is widely used in vehicles, electronics, robotics, industrial control and scientific measurement.

Check Your Understanding

1. What is the Hall Effect?
2. Why do moving charge carriers become separated in a Hall element?
3. What is Hall voltage?
4. In what direction is Hall voltage produced relative to the main current?
5. Explain why charge does not continue accumulating indefinitely on one side of the Hall element.
6. What two forces balance when a steady Hall voltage has developed?
7. Show how E_H = v_dB is obtained for perpendicular motion.
8. State the relationship V_H = IB/(nqt) and identify each quantity.
9. How does increasing current affect Hall voltage?
10. How does increasing magnetic flux density affect Hall voltage?
11. How does increasing carrier density affect Hall voltage?
12. How does decreasing the Hall element's thickness affect Hall voltage?
13. Why are semiconductors particularly useful for Hall Effect sensors?
14. Explain how a Hall probe can measure magnetic flux density.
15. Why is the orientation of a Hall probe important?
16. A Hall sensor produces 15 mV in a 0.20 T field. Assuming a linear response, what voltage would it produce in a 0.60 T field?
17. A wheel containing one magnet produces 30 Hall-sensor pulses per second. Calculate its rotational speed in rpm.
18. Explain how Hall Effect sensors can be used in a brushless DC motor.
19. Explain how a Hall sensor can measure electric current without being directly connected in series with the main circuit.
20. Describe three practical applications of Hall Effect sensors and explain what the sensor detects in each case.