# 22.6 The hall effect  (Page 2/4)

 Page 2 / 4
$\frac{\epsilon }{l}=\text{vB}\text{.}$

Solving this for the Hall emf yields

$\epsilon =\text{Blv}\phantom{\rule{0.25em}{0ex}}\left(B,\phantom{\rule{0.25em}{0ex}}v,\phantom{\rule{0.25em}{0ex}}\text{and}\phantom{\rule{0.25em}{0ex}}l,\phantom{\rule{0.25em}{0ex}}\text{mutually perpendicular}\right),$

where $\epsilon$ is the Hall effect voltage across a conductor of width $l$ through which charges move at a speed $v$ .

One of the most common uses of the Hall effect is in the measurement of magnetic field strength $B$ . 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 $\epsilon$ as shown. Note that the sign of $\epsilon$ depends not on the sign of the charges, but only on the directions of $B$ and $v$ . The magnitude of the Hall emf is $\epsilon =\text{Blv}$ , where $l$ is the pipe diameter, so that the average velocity $v$ can be determined from $\epsilon$ providing the other factors are known.

## 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 $B$ , $v$ , and $l$ are mutually perpendicular, the equation $\epsilon =\text{Blv}$ can be used to find $\epsilon$ .

Solution

Entering the given values for $B$ , $v$ , and $l$ gives

$\begin{array}{lll}\epsilon & =& \text{Blv}=\left(\text{0.100 T}\right)\left(4\text{.}\text{00}×{\text{10}}^{-3}\phantom{\rule{0.25em}{0ex}}m\right)\left(0\text{.200 m/s}\right)\\ & =& \text{80.0 μV}\end{array}$

Discussion

This is the average voltage output. Instantaneous voltage varies with pulsating blood flow. The voltage is small in this type of measurement. $\epsilon$ 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.

## Section summary

• The Hall effect is the creation of voltage $\epsilon$ , known as the Hall emf, across a current-carrying conductor by a magnetic field.
• The Hall emf is given by
$\epsilon =\text{Blv}\phantom{\rule{0.25em}{0ex}}\left(B,\phantom{\rule{0.25em}{0ex}}v,\phantom{\rule{0.25em}{0ex}}\text{and}\phantom{\rule{0.25em}{0ex}}l,\phantom{\rule{0.25em}{0ex}}\text{mutually perpendicular}\right)$
for a conductor of width $l$ through which charges move at a speed $v$ .

## 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.)

## 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 $5\text{.}\text{00}×{\text{10}}^{-5}\text{-T}$ field.

$7\text{.}\text{50}×{\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}V$

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?

(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 $8\text{.}\text{00}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\text{T?}$ (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.

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?

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

A Hall probe calibrated to read $1\text{.}\text{00 μV}$ when placed in a 2.00-T field is placed in a 0.150-T field. What is its output voltage?

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?

$1.\text{16 μV}$

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.)

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

#### Questions & Answers

the definition of photon
8kg of a hot liquid initial T is 90°© is missed with another liquid 3kg at 20° calculate e équilibrium T
8kg of a hot liquid initial T is 90°© is missed with another liquid 3kg at 20° calculate e équilibrium T
Balki
Bright
what are the products when acid and base mixed?
Austin
what work done
work done is the product of force and distance moved in the direction of force
Work done = force (F) * distance (D)
abdulsalam
what is resounance
Abdul
y
Tracy
explain the three laws of isaac Newton with the reference
1st law ; a body will continue to stay at a state of rest or continue to move at a uniform motion on a straight line unless an external force is been acted upon
Austine
3rd law; in every action there is an equal or opposite reaction
Austine
2nd law: F=ma
Austine
why am i not having access to the Link in your exemples /figures ?
what is circut
newtons law of motion
hasiya
First law:In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
Manan
is the ability to do work
Energy
Nwany
u from
Hejreen
any body online hain
Hejreen
ability to do work is energy
what is energy
energy is ability of the capacity to doing work
shafiu
what is vector
A quantity that has both magnitude and direction
Donaldo
can a body with out mass float in space
mosco
Is the quantity that has both magnitude and direction
Amoah
Yes it can float in space,e.g.polyethene has no mass that's why it can float in space
Amoah
that's my suggestion,any other explanation can be given also,thanks
Amoah
A charge of 1.6*10^-6C is placed in a uniform electric field in a density 2*5^10Nc^-1, what is the magnitude of the electric force exerted on the charge?
what's phenomena
Phenomena is an observable fact or event.
Love
Prove that 1/d+1/v=1/f
What interference
What is a polarized light called?
Moyinoluwa
what is a half life
the time taken for a radioactive element to decay by half of its original mass
ken
what is radioactive element
mohammed
Half of the total time required by a radioactive nuclear atom to totally disintegrate
Justice
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
Justice
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
Justice
state the laws of refraction
Fabian
state laws of reflection
Fabian
Why does a bicycle rider bends towards the corner when is turning?
Mac
When do we say that the stone thrown vertically up wards accelerate negatively?
Mac
Give two importance of insulator placed between plates of a capacitor.
Mac
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
Mac
when was the name taken from
retardation of a car
Biola
when was the name retardation taken
Biola
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
Sphere
what's velocity
mosco
Velocity is the rate of change of displacement
Divya