# 22.6 The hall effect  (Page 2/4)

 Page 2 / 4
$\text{qE}=\text{qvB}$

or

$E=\text{vB}.$

Note that the electric field $E$ is uniform across the conductor because the magnetic field $B$ is uniform, as is the conductor. For a uniform electric field, the relationship between electric field and voltage is $E=\epsilon /l$ , where $l$ is the width of the conductor and $\epsilon$ is the Hall emf. Entering this into the last expression gives

$\frac{\epsilon }{l}=\text{vB}\text{.}$

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.

## Test prep for ap courses

An airplane wingspan can be approximated as a conducting rod of length 35 m. As the airplane flies due north, it is flying at a rate of 82 m/s through the Earth’s magnetic field, which has a magnitude of 45 μT toward the north in a direction 57° below the horizontal plane. (a) Which end of the wingspan is positively charged, the east or west end? Explain. (b) What is the Hall emf along the wingspan?

## 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

what is angular velocity
Why does earth exert only a tiny downward pull?
hello
Islam
Why is light bright?
an 8.0 capacitor is connected by to the terminals of 60Hz whoes rms voltage is 150v. a.find the capacity reactance and rms to the circuit
thanks so much. i undersooth well
what is physics
is the study of matter in relation to energy
Kintu
a submersible pump is dropped a borehole and hits the level of water at the bottom of the borehole 5 seconds later.determine the level of water in the borehole
what is power?
power P = Work done per second W/ t. It means the more power, the stronger machine
Sphere
e.g. heart Uses 2 W per beat.
Rohit
A spherica, concave shaving mirror has a radius of curvature of 32 cm .what is the magnification of a persons face. when it is 12cm to the left of the vertex of the mirror
did you solve?
Shii
1.75cm
Ridwan
my name is Abu m.konnek I am a student of a electrical engineer and I want you to help me
Abu
the magnification k = f/(f-d) with focus f = R/2 =16 cm; d =12 cm k = 16/4 =4
Sphere
what do we call velocity
Kings
A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows pa
hi
Godfred
Godfred
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
how can I read physics...am finding it difficult to understand...pls help
try to read several books on phy don't just rely one. some authors explain better than other.
Ju
And don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.
Ju
hope that helps
Ju