<< Chapter < Page Chapter >> Page >

Hall potential measurements show that electrons are the dominant charge carriers in most metals. However, Hall potentials indicate that for a few metals, such as tungsten, beryllium, and many semiconductors, the majority of charge carriers are positive. It turns out that conduction by positive charge is caused by the migration of missing electron sites (called holes) on ions. Conduction by holes is studied later in Condensed Matter Physics .

The Hall effect can be used to measure magnetic fields. If a material with a known density of charge carriers n is placed in a magnetic field and V is measured, then the field can be determined from [link] . In research laboratories where the fields of electromagnets used for precise measurements have to be extremely steady, a “Hall probe” is commonly used as part of an electronic circuit that regulates the field.

Velocity selector

An electron beam enters a crossed-field velocity selector with magnetic and electric fields of 2.0 mT and 6.0 × 10 3 N/C, respectively. (a) What must the velocity of the electron beam be to traverse the crossed fields undeflected? If the electric field is turned off, (b) what is the acceleration of the electron beam and (c) what is the radius of the circular motion that results?


The electron beam is not deflected by either of the magnetic or electric fields if these forces are balanced. Based on these balanced forces, we calculate the velocity of the beam. Without the electric field, only the magnetic force is used in Newton’s second law to find the acceleration. Lastly, the radius of the path is based on the resulting circular motion from the magnetic force.


  1. The velocity of the unperturbed beam of electrons with crossed fields is calculated by [link] :
    v d = E B = 6 × 10 3 N / C 2 × 10 −3 T = 3 × 10 6 m / s.
  2. The acceleration is calculated from the net force from the magnetic field, equal to mass times acceleration. The magnitude of the acceleration is:
    m a = q v B a = q v B m = ( 1.6 × 10 −19 C ) ( 3 × 10 6 m/s ) ( 2 × 10 −3 T ) 9.1 × 10 −31 kg = 1.1 × 10 15 m/s 2 .
  3. The radius of the path comes from a balance of the circular and magnetic forces, or [link] :
    r = m v q B = ( 9.1 × 10 −31 kg ) ( 3 × 10 6 m/s ) ( 1.6 × 10 −19 C ) ( 2 × 10 −3 T ) = 8.5 × 10 −3 m.


If electrons in the beam had velocities above or below the answer in part (a), those electrons would have a stronger net force exerted by either the magnetic or electric field. Therefore, only those electrons at this specific velocity would make it through.

Got questions? Get instant answers now!

The hall potential in a silver ribbon

[link] shows a silver ribbon whose cross section is 1.0 cm by 0.20 cm. The ribbon carries a current of 100 A from left to right, and it lies in a uniform magnetic field of magnitude 1.5 T. Using a density value of n = 5.9 × 10 28 electrons per cubic meter for silver, find the Hall potential between the edges of the ribbon.

The silver ribbon is shown with current flowing to the right, a magnetic field pointing up, negative charges accumulating on the edge near us and positive charges accumulating on the far edge. The dimensions of the strip are 1.0 cm by 0.20 cm.
Finding the Hall potential in a silver ribbon in a magnetic field is shown.


Since the majority of charge carriers are electrons, the polarity of the Hall voltage is that indicated in the figure. The value of the Hall voltage is calculated using [link] :

V = I B l n e A .


When calculating the Hall voltage, we need to know the current through the material, the magnetic field, the length, the number of charge carriers, and the area. Since all of these are given, the Hall voltage is calculated as:

V = I B l n e A = ( 100 A ) ( 1.5 T ) ( 1.0 × 10 −2 m ) ( 5.9 × 10 28 / m 3 ) ( 1.6 × 10 −19 C ) ( 2.0 × 10 −5 m 2 ) = 7.9 × 10 −6 V.


As in this example, the Hall potential is generally very small, and careful experimentation with sensitive equipment is required for its measurement.

Got questions? Get instant answers now!

Check Your Understanding A Hall probe consists of a copper strip, n = 8.5 × 10 28 electrons per cubic meter, which is 2.0 cm wide and 0.10 cm thick. What is the magnetic field when I = 50 A and the Hall potential is (a) 4.0 μ V and (b) 6.0 μ V ?

a. 1.1 T; b. 1.6 T

Got questions? Get instant answers now!


  • Perpendicular electric and magnetic fields exert equal and opposite forces for a specific velocity of entering particles, thereby acting as a velocity selector. The velocity that passes through undeflected is calculated by v = E B .
  • The Hall effect can be used to measure the sign of the majority of charge carriers for metals. It can also be used to measure a magnetic field.

Conceptual questions

Hall potentials are much larger for poor conductors than for good conductors. Why?

Poor conductors have a lower charge carrier density, n , which, based on the Hall effect formula, relates to a higher Hall potential. Good conductors have a higher charge carrier density, thereby a lower Hall potential.

Got questions? Get instant answers now!


A strip of copper is placed in a uniform magnetic field of magnitude 2.5 T. The Hall electric field is measured to be 1.5 × 10 −3 V/m . (a) What is the drift speed of the conduction electrons? (b) Assuming that n = 8.0 × 10 28 electrons per cubic meter and that the cross-sectional area of the strip is 5.0 × 10 −6 m 2 , calculate the current in the strip. (c) What is the Hall coefficient 1/nq?

Got questions? Get instant answers now!

The cross-sectional dimensions of the copper strip shown are 2.0 cm by 2.0 mm. The strip carries a current of 100 A, and it is placed in a magnetic field of magnitude B = 1.5 T. What are the value and polarity of the Hall potential in the copper strip?

A horizontal 2.0 cm by 2.0 cm square copper strip has current I flowing through it to the right. A magnetic field, B, points up, perpendicular to the face of the strip.

5.8 × 10 −7 V

Got questions? Get instant answers now!

The magnitudes of the electric and magnetic fields in a velocity selector are 1.8 × 10 5 V/m and 0.080 T, respectively. (a) What speed must a proton have to pass through the selector? (b) Also calculate the speeds required for an alpha-particle and a singly ionized s O 16 atom to pass through the selector.

Got questions? Get instant answers now!

A charged particle moves through a velocity selector at constant velocity. In the selector, E = 1.0 × 10 4 N/C and B = 0.250 T. When the electric field is turned off, the charged particle travels in a circular path of radius 3.33 mm. Determine the charge-to-mass ratio of the particle.

4.8 × 10 7 C/kg

Got questions? Get instant answers now!

A Hall probe gives a reading of 1.5 μ V for a current of 2 A when it is placed in a magnetic field of 1 T. What is the magnetic field in a region where the reading is 2 μ V for 1.7 A of current?

Got questions? Get instant answers now!

Questions & Answers

determining dimensional correctness
determine dimensional correctness of,T=2π√L/g
somebody help me answer the question above
calculate the heat flow per square meter through a mineral roll insulation 5cm thick if the temperature on the two surfaces are 30degree Celsius and 20 degree Celsius respectively. thermal conduction of mineral roll is 0.04
akuribire Reply
what are the elementary compositions of a cell?
jackson Reply
when a current pass through a material does the velocity varies
lovet Reply
what is spin entropy ?and disorder in ferromagnetic material
Nepal Reply
diagram of an hall effect sensor
Aweda Reply
if a magnetised wire having dipole moment M is bent in the form of arc subtending angle of 45°at centre,new magnetic moment is
Pravin Reply
is this book for preparing IIT or neet?
jyotirmayee Reply
is it possible to increase the temperature of a gas without adding heat to it?
gurpreet Reply
I'm not sure about it, but I think it's possible. If you add some form of energy to the system, it's a possibility. Also, if you change the pression or the volume of the system, you'll increase the kinetic energy of the system, increasing the gas temperature. I don't know if I'm correct.
For example, if you get a syringe and close the tip(sealing the air inside), and start pumping the plunger, you'll notice that it starts getting hot. Again, I'm not sure if I am correct.
you are right for example an adiabatic process changes all variables without external energy to yield a temperature change. (Search Otto cycle)
when a current pass through a material does the velocity varies
yes at adiabatic compression temperature increase
how to draw a diagram of a triode
Ssempala Reply
whate is fckg diagrame?
why do we use integration?
Monalisa Reply
To know surfaces below graphs.
To find a Primitive function. Primitive function: a function that is the origin of another
what is laps rate
Г=-dT/dZ that is simply defination
what is z
to find the area under a graph or to accumulate .e.g. sum of momentum over time is no etic energy.
Z is alt.,dZ altv difference
what is the Elasticty
Heeran Reply
it is the property of the by virtue of it regains it's original shape after the removal of applied force (deforming force).
property of the material
which type of cable is suitable for patrol station wiring
Eric Reply
what is calorimeter
odionyenma Reply
heat measuring device
What is mean electric potential
Biren Reply
Practice Key Terms 2

Get the best University physics vol... course in your pocket!

Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?