DefinitionThe Hall effect is the production of a voltage difference (the Hall voltage) across a current carrying conductor (in presence of magnetic field), perpendicular to both current and the magnetic field.

DiscoveryThe Hall effect was discovered in 1879 by Edwin Herbert Hall while working on his doctoral degree at the Johns Hopkins University in Baltimore, Maryland, USA.

EDWIN H. HALL

Theory• A static magnetic field has no effect on

a charged particle unless it is moving.

• When charges flow, a mutually perpendicular force (Lorentz force) is induced on the charge.

• Now electrons and holes are separated by opposite force.

Theory• This produces a electric field which

depends upon cross product of magnetic intensity [H] and current density [J]

Eh=R(JxH)• R is called Hall Coefficient• Consider a Semiconductor bar along X-

axis, Magnetic field along Z-axis. Thus Eh will be along Y-axis.

• Thus R=Vh/aJH=Vhb/IH

• Vh is Hall Voltage and I is Jab

Electrons flowing without a magnetic fieldElectrons flowing without a magnetic field

t

d

semiconductor slice

+ _

I I

When the magnetic field is When the magnetic field is turned on ..turned on ..

B-field

I qBv

As time goes by...As time goes by...

I

qBv = qElowpotential

highpotential

qE

Finally...Finally...

B-field

I

VH

Hall Probes

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Via LessEMF.comVia the NDT Resource Center

Richard Beck - Physics 141A, 2013

A Visual Representation

14

From Non-Destructive Testing (NDT) Resource Center

Richard Beck - Physics 141A, 2013

Hole ELECTRON

ElectromagnetGaussmeter

Hall Probe

SetupDigital hall effect setup

Working1. Conductor is kept

in a magnetic field.

2. Current is passed through it.

3. We get a reading in voltmeter kept perpendicular to the conductor.

Recording Observation• After setup the

Hall Voltage is measured as a function of –

1. Current keeping magnetic field constant.

2. Magnetic field keeping current constant.

Current

Hal

l Vol

tage

Conclusions1. Hall Coefficient can be determined using

Rh=Vhb/IH

2. Hall effect can be used to determine the signs of current carrier in metals and semiconductor.

3. A straight graph between Hall voltage & Current and between Hall voltage & Magnetic field confirms their linear relationship. This point has important meaning as hall effect can be effectively used to determine current or magnetic field, when other is known.

Precautions1. Hall Voltage should be measured very

carefully and accurately.2. Distance between pole pieces of

Electromagnet should not be changed during the whole experiment.

3. Current passing through semiconductor slab should be strictly within permissible limit.

ApplicationsHall effect devices produce a very low signal level and thus require amplification. In early 20th century vacuum tube amplifiers were expensive and unreliable. But with the development of the low cost integrated circuit the Hall effect sensor became suitable for mass application.

Current Sensor• When electrons flow through

a conductor, a magnetic field is produced.

• Thus, it is possible to create a non-contacting current sensor. This has several advantages:1. No additional resistance (a

shunt) need be inserted in the primary circuit.

2. Also, the voltage present on the line to be sensed is not transmitted to the sensor, which enhances the safety of measuring equipment.

Hall effect current sensor with internal integrated circuit amplifier.

Electric Motor ControlSome types of brushless DC electric motors use Hall effect sensors to detect the position of the rotor and feed that information to the motor controller. This allows for more precise motor control.

Magnetometer• Smart phones like iPhone

3GS are equipped with magnetic compass.

• These compass measure Earth‘s magnetic field using 3-axis magnetometer.

• These magnetometer are sensors based on Hall Effect.

• These sensors produce a voltage proportional to the applied magnetic field and also sense polarity.

Blood FlowSimilar to the Hall effect, the velocity of blood

can be measured by its ions.

next

Hallresistance-Rxy(ohms)

The classical Hall effect

• Lorentz force likes to deflect jx• However, E-field is set up which balances Lorentz force

• Balance occurs when Ey = vxBz = Vy/ly• But jx = nevx (or ix = nevxAx)

⇒ Rxy = Vy / ix = RH Bz × (ly /Ax), where RH = 1/ne

Where ly is transverse width of sample and Ax is the transverse cross sectional areaof the sample, i.e. depends on shape of sample

0 2 4 6 8 10

200

0

1200

1000

800

600

400

1400

Slope related to RH

and sample dimensions

Magnetic field (tesla)

Ax

ly

Reminder: The Lorentz Force

F = q[E + (v × B)]

In Cars

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• Used expansively in rotating systems

• Anti-lock brakes, motor feedback, ignition

Via Power Systems Design, Ltd. Via Draper, 2005

Richard Beck - Physics 141A, 2013

In Space• Hall Effect thruster

• Trap electrons in a magnetic field, electrons ionize propellant, creates thrust

Richard Beck - Physics 141A, 2013 31

And there are many more applications of hall effect…