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ε l = vB . size 12{ { {ε} over {l} } = ital "vB" "." } {}

Solving this for the Hall emf yields

ε = Blv ( B , v , and l , mutually perpendicular ) , size 12{ε= ital "Blv"``` \( B,`v,`"and"`l,`"mutually perpendicular" \) ,} {}

where ε size 12{ε} {} is the Hall effect voltage across a conductor of width l size 12{l} {} through which charges move at a speed v size 12{v} {} .

Diagram showing an electron moving to the left in a three-dimensional rectangular space with velocity v. The magnetic field is oriented out of the page. The electric field is down. The electric force on the charge is up while the magnetic force on the charge is down. An illustration of the right hand rule shows the thumb pointing to the left with v, the fingers out of the page with B, and the force on a positive charge up and away from the palm.
The Hall emf ε size 12{ε} {} produces an electric force that balances the magnetic force on the moving charges. The magnetic force produces charge separation, which builds up until it is balanced by the electric force, an equilibrium that is quickly reached.

One of the most common uses of the Hall effect is in the measurement of magnetic field strength B size 12{B} {} . Such devices, called Hall probes , can be made very small, allowing fine position mapping. Hall probes can also be made very accurate, usually accomplished by careful calibration. Another application of the Hall effect is to measure fluid flow in any fluid that has free charges (most do). (See [link] .) A magnetic field applied perpendicular to the flow direction produces a Hall emf ε size 12{ε} {} as shown. Note that the sign of ε size 12{ε} {} depends not on the sign of the charges, but only on the directions of B size 12{B} {} and v size 12{v} {} . The magnitude of the Hall emf is ε = Blv size 12{ε= ital "Blv"} {} , where l size 12{l} {} is the pipe diameter, so that the average velocity v size 12{v} {} can be determined from ε size 12{ε} {} providing the other factors are known.

Diagram showing a tube with diameter l with one end between the north and south poles of a magnet. The charges are moving with velocity v within the tube and out of the page. The magnetic field B is oriented across the tube, from the north to the south pole of the magnet. The force on the charges is up for positive charges and down for negative charges. e m f = B l v.
The Hall effect can be used to measure fluid flow in any fluid having free charges, such as blood. The Hall emf ε size 12{ε} {} is measured across the tube perpendicular to the applied magnetic field and is proportional to the average velocity v size 12{v} {} .

Calculating the hall emf: hall effect for blood flow

A Hall effect flow probe is placed on an artery, applying a 0.100-T magnetic field across it, in a setup similar to that in [link] . What is the Hall emf, given the vessel’s inside diameter is 4.00 mm and the average blood velocity is 20.0 cm/s?

Strategy

Because B size 12{B} {} , v size 12{v} {} , and l size 12{l} {} are mutually perpendicular, the equation ε = Blv size 12{ε= ital "Blv"} {} can be used to find ε size 12{ε} {} .

Solution

Entering the given values for B size 12{B} {} , v size 12{v} {} , and l size 12{l} {} gives

ε = Blv = 0.100 T 4 . 00 × 10 3 m 0 .200 m/s = 80.0 μV alignl { stack { size 12{ε= ital "Blv"= left (0 "." "100"`T right ) left (4 "." "00" times "10" rSup { size 8{ - 3} } `m right ) left (0 "." "200"`"m/s" right )} {} # ="80" "." 0`"μV" {}} } {}

Discussion

This is the average voltage output. Instantaneous voltage varies with pulsating blood flow. The voltage is small in this type of measurement. ε size 12{ε} {} is particularly difficult to measure, because there are voltages associated with heart action (ECG voltages) that are on the order of millivolts. In practice, this difficulty is overcome by applying an AC magnetic field, so that the Hall emf is AC with the same frequency. An amplifier can be very selective in picking out only the appropriate frequency, eliminating signals and noise at other frequencies.

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Section summary

  • The Hall effect is the creation of voltage ε size 12{ε} {} , known as the Hall emf, across a current-carrying conductor by a magnetic field.
  • The Hall emf is given by
    ε = Blv ( B , v , and l , mutually perpendicular ) size 12{ε= ital "Blv"``` \( B,`v,`"and"`l,`"mutually perpendicular" \) } {}
    for a conductor of width l size 12{l} {} through which charges move at a speed v size 12{v} {} .

Conceptual questions

Discuss how the Hall effect could be used to obtain information on free charge density in a conductor. (Hint: Consider how drift velocity and current are related.)

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Problems&Exercises

A large water main is 2.50 m in diameter and the average water velocity is 6.00 m/s. Find the Hall voltage produced if the pipe runs perpendicular to the Earth’s 5 . 00 × 10 5 -T size 12{5 "." "00" times "10" rSup { size 8{ - 5} } "-T"} {} field.

7 . 50 × 10 4 V

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What Hall voltage is produced by a 0.200-T field applied across a 2.60-cm-diameter aorta when blood velocity is 60.0 cm/s?

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(a) What is the speed of a supersonic aircraft with a 17.0-m wingspan, if it experiences a 1.60-V Hall voltage between its wing tips when in level flight over the north magnetic pole, where the Earth’s field strength is 8 . 00 × 10 5 T? size 12{8 "." "00" times "10" rSup { size 8{ - 5} } `"T?"} {} (b) Explain why very little current flows as a result of this Hall voltage.

(a) 1.18 × 10 3 m/s

(b) Once established, the Hall emf pushes charges one direction and the magnetic force acts in the opposite direction resulting in no net force on the charges. Therefore, no current flows in the direction of the Hall emf. This is the same as in a current-carrying conductor—current does not flow in the direction of the Hall emf.

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A nonmechanical water meter could utilize the Hall effect by applying a magnetic field across a metal pipe and measuring the Hall voltage produced. What is the average fluid velocity in a 3.00-cm-diameter pipe, if a 0.500-T field across it creates a 60.0-mV Hall voltage?

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Calculate the Hall voltage induced on a patient’s heart while being scanned by an MRI unit. Approximate the conducting path on the heart wall by a wire 7.50 cm long that moves at 10.0 cm/s perpendicular to a 1.50-T magnetic field.

11.3 mV

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A Hall probe calibrated to read 1 . 00 μV size 12{1 "." "00"`"μV"} {} when placed in a 2.00-T field is placed in a 0.150-T field. What is its output voltage?

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Using information in [link] , what would the Hall voltage be if a 2.00-T field is applied across a 10-gauge copper wire (2.588 mm in diameter) carrying a 20.0-A current?

1. 16 μV size 12{1 "." "47"`"μV"} {}

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Show that the Hall voltage across wires made of the same material, carrying identical currents, and subjected to the same magnetic field is inversely proportional to their diameters. (Hint: Consider how drift velocity depends on wire diameter.)

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A patient with a pacemaker is mistakenly being scanned for an MRI image. A 10.0-cm-long section of pacemaker wire moves at a speed of 10.0 cm/s perpendicular to the MRI unit’s magnetic field and a 20.0-mV Hall voltage is induced. What is the magnetic field strength?

2.00 T

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Questions & Answers

How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
Larissa Reply
How do you convert 0.0045kgcm³ to the si unit?
EDYKING Reply
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
Falana Reply
I only know 5: •Solids •Liquids •Gases •Plasma •Bose-Einstein condensate
Thapelo
Alright Thank you
Falana
Which one is the Bose-Einstein
James
can you explain what plasma and the I her one you mentioned
Olatunde
u can say sun or stars are just the state of plasma
Mohit
but the are more than seven
Issa
what the meaning of continuum
Akhigbe Reply
What state of matter is fire
Thapelo Reply
fire is not in any state of matter...fire is rather a form of energy produced from an oxidising reaction.
Xenda
Isn`t fire the plasma state of matter?
Walter
all this while I taught it was plasma
Victor
How can you define time?
Thapelo Reply
Time can be defined as a continuous , dynamic , irreversible , unpredictable quantity .
Tanaya
unpredictable? but I can say after one o'clock its going to be two o'clock predictably!
Victor
what is the relativity of physics
Paul Reply
How do you convert 0.0045kgcm³ to the si unit?
flint
What is the formula for motion
Anthony Reply
V=u+at V²=u²-2as
flint
S=ut+½at
flint
they are eqns of linear motion
King
S=Vt
Thapelo
v=u+at s=ut+at^\2 v^=u^+2as where ^=2
King
hi
Mehadi
hello
King
Explain dopplers effect
Jennifer Reply
Not yet learnt
Bob
Explain motion with types
Bob
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
Alabi Reply
Scalar quantity Because acceleration has only magnitude
Bob
acleration is vectr quatity it is found in a spefied direction and it is product of displcemnt
bhat
its a scalar quantity
Paul
velocity is speed and direction. since velocity is a part of acceleration that makes acceleration a vector quantity. an example of this is centripetal acceleration. when you're moving in a circular patter at a constant speed, you are still accelerating because your direction is constantly changing.
Josh
acceleration is a vector quantity. As explained by Josh Thompson, even in circular motion, bodies undergoing circular motion only accelerate because on the constantly changing direction of their constant speed. also retardation and acceleration are differentiated by virtue of their direction in
fitzgerald
respect to prevailing force
fitzgerald
What is the difference between impulse and momentum?
Manyo
Momentum is the product of the mass of a body and the change in velocity of its motion. ie P=m(v-u)/t (SI unit is kgm/s). it is literally the impact of collision from a moving body. While Impulse is the product of momentum and time. I = Pt (SI unit is kgm) or it is literally the change in momentum
fitzgerald
Or I = m(v-u)
fitzgerald
the tendency of a body to maintain it's inertia motion is called momentum( I believe you know what inertia means) so for a body to be in momentum it will be really hard to stop such body or object..... this is where impulse comes in.. the force applied to stop the momentum of such body is impulse..
Pelumi
Calculation of kinetic and potential energy
dion Reply
K.e=mv² P.e=mgh
Malia
K is actually 1/2 mv^2
Josh
what impulse is given to an a-particle of mass 6.7*10^-27 kg if it is ejected from a stationary nucleus at a speed of 3.2*10^-6ms²? what average force is needed if it is ejected in approximately 10^-8 s?
John
speed=velocity÷time velocity=speed×time=3.2×10^-6×10^-8=32×10^-14m/s impulse [I]=∆momentum[P]=mass×velocity=6.7×10^-27×32×10^-14=214.4×10^-41kg/ms force=impulse÷time=214.4×10^-41÷10^-8=214.4×10^-33N. dats how I solved it.if wrong pls correct me.
Melody
what is sound wave
Nworu Reply
sound wave is a mechanical longitudinal wave that transfers energy from one point to another
Ogor
its a longitudnal wave which is associted wth compresion nad rearfractions
bhat
what is power
PROMISE Reply
it's also a capability to do something or act in a particular way.
Kayode
Newton laws of motion
Mike
power also known as the rate of ability to do work
Slim
power means capabilty to do work p=w/t its unit is watt or j/s it also represents how much work is done fr evry second
bhat
what does fluorine do?
Cheyanne Reply
strengthen and whiten teeth.
Gia
a simple pendulum make 50 oscillation in 1minute, what is it period of oscillation?
Nansing Reply
length of pendulm?
bhat
Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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