# What is Hall effect: Definition and 131 Discussions

The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor that is transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current. It was discovered by Edwin Hall in 1879.A Hall effect can also occur across a void or hole in a semiconductor or metal plate, when current is injected via contacts that lie on the boundary or edge of the void or hole, and the charge flows outside the void or hole, in the metal or semiconductor. This Hall effect becomes observable in a perpendicular applied magnetic field across voltage contacts that lie on the boundary of the void on either side of a line connecting the current contacts, it exhibits apparent sign reversal in comparison to the standard ordinary Hall effect in the simply connected specimen, and this Hall effect depends only on the current injected from within the void.Superposition may also be realized in the Hall effect: Imagine the standard Hall configuration, a simply connected (void-less) thin rectangular homogeneous Hall plate with current and voltage contacts on the (external) boundary which develops a Hall voltage in a perpendicular magnetic field. Now, imagine placing a rectangular void or hole within this standard Hall configuration, with current and voltage contacts, as mentioned above, on the interior boundary or edge of the void. For simplicity, the current contacts on the boundary of the void may be lined up with the current contacts on the exterior boundary in the standard Hall configuration. In such a configuration, two Hall effects may be realized and observed simultaneously in the same doubly connected device: A Hall effect on the external boundary that is proportional to the current injected only via the outer boundary, and an apparently sign reversed Hall effect on the interior boundary that is proportional to the current injected only via the interior boundary. Multiple Hall effects superposition may be realized by placing multiple voids within the Hall element, with current and voltage contacts on the boundary of each void. DE Patent 4308375
The Hall coefficient is defined as the ratio of the induced electric field to the product of the current density and the applied magnetic field. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of the charge carriers that constitute the current.
For clarity, the original effect is sometimes called the ordinary Hall effect to distinguish it from other "Hall effects", which may have additional physical mechanisms, but build on these basics.

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1. ### I Quantum Hall Effect and Hall Voltage

I understand that the Quantum Hall Effect explains how both the transverse and longitudinal resistance vary with magnetic field strength. I don’t get why the hall resistance is equal to the hall voltage over the current . I know current isn’t a vector quantity but isn’t the hall resistance an...
2. ### A What is the correct form of the Berry curvature formula?

I am studying Berry curvature for a specific material and faced different types of the Berry curvature formula. Some papers use only valence eigenstates (u1) like this i∗(<(∂U1/∂kx)|(∂U1/∂ky)>−<(∂U1/∂ky)|(∂U1/∂kx)>) and someone uses summation on all the conduction and valence bands like this...
3. ### I Hall effect -- is it always applicable?

A current carrying conductor experiences magnetic force in a magnetic field. F=BILsinθ Where, B = Magnetic flux density I = Current L = Length of conductor and θ = Angle between magnetic field and current This force is due to free electrons moving in a...
4. ### Dependence of Hall coefficient on temperature in semiconductors

My first assumption is that the temperature dependence on the mobilities can be neglected, and so we would have: $$R_H(T)= \frac{1}{e} \frac{p_v(T)\mu_h^2-n_c(T)\mu_e^2}{(p_v(T)\mu_h+n_c(T)\mu_e)^2}$$ The expression for the electron and hole densities could be derived from...
5. ### I Question on Hall Effect and magnetic force

so with a Hall Voltage, you have positive current traveling upwards in a wire in the +y-direction and a magnetic field into the screen in the -z-direction. the right hand rule has positive charge deflecting to the left. now if you look at the drift velocity of electrons moving downward in the...
6. ### Hall effect over a conducting ring

This is the diagram provided in the question: The ring is made of conducting material. I was originally asked to find the potential difference between ##a## and ##b##. I did so using the Hall effect (and assuming it would work as per normal in this situation). This got me ##\Delta V = vBl##...
7. ### A Quantum Hall Effect Basics: Topological Insulator & Semi-Metal

I need them short. I need them so I can understand the basics of topological insulator and semi-metal.
8. ### Edge States in Integer Quantum Hall Effect (IQHE)

Hello there, I am having trouble understanding what parts b-d of the question are asking. By solving the Schrodinger equation I got the following for the Landau Level energies: $$E_{n,k} = \hbar \omega_H(n+\frac 12)+\frac {\hbar^2k^2}{2m}\frac{\omega^2}{\omega_H^2}$$ Where ##\omega_H =...
9. ### I Why Is the Anomalous Hall Coefficient Temperature Dependent?

Hi! Reading through this paper, the Hall resistivity in ferromagnetic materials is given by $$\rho_H = R_0 B + 4 \pi R_s M$$ It is mentioned that ##R_s## (anomalous Hall coefficient) is significantly larger than ##R_0## (ordinary Hall coefficient) and has a strong dependence on temperature...
10. ### I How Does Increasing Length Affect Spin Hall Voltage in Materials?

Hi! I'm trying to understand the dependence of spin hall voltage on various parameters of the material. I have been going through this paper, and it is mentioned that $$V_{SH} = 2 \pi R_s L j_x n \mu_B$$ In the equation, only ##L## and ##j_x## seem to be the variables. Does increasing ##L##...
11. ### I Distribution of charges as a result of the Hall Effect

Circuit runs from q0 to q1, some E field (our charge source/sink) 1. Is the current running from q0 to q1 impacted by the existence of the B field? For example, if there were no B field, current would flow from q0 to q1, let's call it I0. When we flip on the B field what effect is there on the...
12. ### Is the Hall Effect Weaker in Semiconductors Due to Limited Energy States?

How does the Hall effect work in semiconductors. Since the there aren't enough availabe energy states in the valence band to hold all electrons trying to move due to the magnetic field the Hall effect must be weaker correct?
13. ### I Solid State Physics: Explaining Ashcroft & Mermin's Hall Effect

Could anyone please explain the differnce between these two picture of Ashcroft & Mermin solid state physics book: Why in these two pictures the + and - signs don't compatible with each other?! I think in the pic12-11 the signs don't draw correctly. It must be vice versa I mean + signs in left...
14. ### I Hall Effect constant and Cyclotron frequency

In the ch1 if solid state physics Mermin & Ashcroft, in the hall effect section these paragraph are about cyclotron frequency, but what the two last terms want to say(the screen shot of the page is attached)? And I can't understand what happens to hall constant in high-field regime?
15. ### I How does the Hall effect interact with the iLB force in a copper wire?

A current is flowing in a copper wire (electrons are flowing). The electrons will be deflected to the left wall of the wire due to Hall effect. They leave on the right wall of the wire a deficit of electrons, leaving them positively charged, so there’s a voltage difference between the left and...
16. ### Does the quantum Hall effect come under the category condensed matter?

Title? Thanks. I think it does since these do : - Quasi particles - Collective behaviour of particles - Phase transitions Any others?
17. ### A Edge state question for a 2-D material and the quantum Hall effect

I have read some materials about quantum hall effect and know that at the edge of a 2D material , one can linearize the potential V and the linear dispersion relation represents right/left moving fermion. So , Can I say that for a given hamiltonian , if I can linearizae it at edge, then this...
18. ### A Difference of the spin Hall effect in intrinsic and extrinsic semiconductors?

Hello there, I don't really get the difference between the extrinsic or intrinsic spin hall effect or contribution. As i understand, in extrinsic you have spin scattering by impurities, so its the spin orbit interaction of the spin with its orbit, and this orbit is influenced by an impurity...
19. ### A E-writing Action on a different slice of space-time, Quantum Hall Effect

Hi, I'm looking at QHE notes D.Tong and wondering how he gets from equation 5.46 to 5.48 ( http://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf ) ##S_{CS}=\frac{k}{4\pi}\int d^3 x \epsilon^{\mu \nu \rho} tr(a_{\mu}\partial_{\nu}a_{\rho} -\frac{2i}{3}a_{\mu}a_{\nu}a_{\rho})##. manifold ## \bf{R}...
20. ### A Rashba-Effect and Intrinsic Spin Hall Effect

Hello everybody, Im looking for a good explanation for the Rashba effect or Rashba Spin Orbit coupling (when it is the same effect with 2 names?) . If somebody can help me here that would be awesome. Moreover i try to understand the intrinsic mechanism of the Spin Hall Effect with the Berry...
21. ### A Fractional Quantum Hall Effect- degeneracy of ground state (Tong's notes)

Hi , I'm looking at the argument in David Tongs notes (http://www.damtp.cam.ac.uk/user/tong/qhe/three.pdf) for ground state degeneracy on depending on the topology of the manifold (page 97, section 3.2.4). I follow up to getting equation 3.31 but I'm stuck on the comment after : ' But such an...
22. ### Is it possible to connect a Hall Effect Flow Sensor output to a PLC?

Hello guys, I am building a small prototype for a Coolant Dispensing System and need to measure the flow rate of water & chemical in the pipe in order to control the opening of valves downstream. Since I am building a small pilot system, I can't really spend too much money and hence I intend...
23. ### Where does the energy come from in the potential difference in the Hall effect?

Where does energy come from in potential difference appearing in Hall effect?It is magnetic force causes this potential.But we know that magnetic force does not do work on motion charge particles, then where is the energy come from?It seems contradiction that magnetic forces cause the potential...
24. ### A Why do conductivities and resistivities change with magnetic field strength?

Greetings, assume we have a 2-dimensional system in the x-y-plane. An electric field is applied in x-direction, a magnetic field is applied in z-direction. As is well-known, the charge carriers get pushed in the y-direction due to the Lorentz-force until the Hall field is strong enough to...
25. ### Textbook says V=E/w but units don't match

In my textbook, it is talking about the Hall Effect on a flat conductor with width w carrying a current i in a uniform magnetic field perpendicular to the plane of the strip. It says that this will create a potential difference of V=E/w where E is the induces electric field from the electrons...
26. ### Find the magnetic field given I, t, Hall EMF, and G_s

Hi! I had this problem for homework (Mastering Physics), and I'm not sure what I'm doing incorrectly. Is there something fundamental that I'm misunderstanding? Each time I do this, I get 0.717136.. T as my solution 1. Homework Statement I = 12.6 A w = 0.0142 m t = 0.00122 m E_H = 1.82 *...
27. ### I Charge carrier density: Hall experiment vs Fermi-Dirac statistics

Many times, the charge carrier density of a material is determined from a Hall effect experiment, from ##R_H=1/(ne)## (SI units). Where ##R_H## is determined from a measured voltage and other controllable parameters. As far as I know, this simple formula comes from the obsolete Drude's model...
28. ### A High-field Hall effect and magnetoresistance

I'm reading Mermin's Solid State Physics, chapter 12: The semiclasssical model of electron dynamics. I know the current density from the ##n## band is $$\mathbf{j}=(-e)\int_{\text{occupied}}f(\epsilon_{\text{n}}(\mathbf{k}))\frac{d\mathbf{k}}{4\pi^3}\mathbf{v}_{\text{n}}(\mathbf{k}).$$ In...
29. ### A Why do we need to know "two-bands" Hall coefficient and magn

(Oh my god, why can't my post show normally? Some sentences just disappear, but I can still see them while editing. It's very weird. Can someone help me? I've reported.)I know only partially filled bands result in current density, and I think there must be not only 2 partially filled bands, but...
30. ### A Why is ##\omega_c \tau >>1## for several revolutions?

Hey, I read about charge carriers in semiconductors in a magnetic field. They write that for several revolutions ##\omega_c \tau >>1## holds. But I think for one revolution it is ##\omega_c \tau = 2 \pi##. (##\tau## is the scattering time) Why they do not write ##\omega_c \tau >> 2 \pi##...
31. ### Why does the trig expression just disappear?

Homework Statement Homework Equations 3. Solution Then the equations from part (A) are used--but why does the converted trig (1-cos(etc)) go away? Does this have to do with the mean-squared bit?
32. ### I What Caused the Lower Resistance in the Second Graph?

Hi, in laboratory i had a sample of Ge with p-doping. In a first place i have done different measure V vs I (first image) Then i insert the sample in a magnetic field perpendicular to the sample. And i have done measure of V vs B (with a fixed current at 8 mA) and i obtained the second image...
33. ### I How Does Spin Hall Effect Couple Charge and Spin Current?

Hi, I have been trying to understand how the spin hall effect comes about. However, everywhere I look I just find 'the spin-orbit interaction couples the charge and spin current'. I really don't understand how does the current couple through the interaction. Any help would be much appreciated...
34. ### Hall Effect in an alternating current circuit

Since the classical Hall EMF is proportional to current, in an alternating current circuit, the Hall Emf should also follow an alternating pattern. Is it so? Or the Hall Emf doesn't change in a sine wave pattern instead remains more or less same and has a voltage based on the average/rms...
35. ### Charge Carriers in the Hall Effect

For a lab I just finished this past week, we were working with the hall effect and finding hall voltages. The metals used were p-germanium and n-germanium semi-conductors. I understand why in n-germanium the hall voltage is positive and p-germanium is negative assuming negative charge carriers...
36. ### Solid State Books on the Integer Quantum Hall effect

Hi, does anybody know of any good sources to learn about the Integer Quantum Hall effect from the perspective of theoretical physics? Any suggestion will be appreciated, thanks.
37. S

### What are the Best Methods for Precise Vertical Movement Measurement?

I want to test the accuracy a linear displacement sensor (Hall effect) that I have, but I'm not sure what to measure it against. The sensors are made to measure with a resolution of 10μm. My initial thought was to use a drill press to move up and down, but I don't think I know of any that are...
38. S

### What magnetic position sensor to choose?

I want to record the displacement of a small magnetic ball moving sideways across the face of the sensor. I've had a close look at AMS's catalog of magnetic position sensors and I'm not sure how to choose one. If I'm working with a movement range of <5mm and want a resolution of 5-10μm, and...
39. ### I Longitudinal resistivity in Integer Quantum Hall Effect

I have studied the integer quantum hall effect mainly from David Tong's notes and i understand how the ## \rho_{xy}## is quantized in terms of the chern number. What I don't understand is - how the chern numbers relate to the number of filled Landau levels though. - I also don't understand the...
40. ### A Why the physical meaning of the quantum Hall effect is important

I have read some paper about transport measurement of graphene. From classical hall effect, we can get some information about kind of charge carrier, charge density etc. So, it is important for understanding matter. But, I don`t know why quantum hall effect is important in graphene transport...
41. ### I Hall Effect & Magnetic Induction Explained

Can someone explain in detail if halls effect is magnetic induction?
42. ### Engineering Finding the Total Force on the Circuit Loop

Homework Statement The problem asks to find the Total Force on the Circuit Loop. I have a circuit loop with length 30.0 cm and width 10.0 cm with a current I2= 30.0 A that is flowing counter-clockwise. There is a wire that has the current I1=15.0 A flowing from left to right and is 7.50 cm from...
43. ### I Hall Effect: Electric Field Direction at Equilibrium

I have a good understanding on the hall effect. However, I was told by my tutor that the electric field direction at equilibrium remains pointing in the negative side of the conducting material and the force it generated is canceled out. But further reading online text, the electric field...
44. ### A Hall coefficient's finite temperature experiments in metals

There are lots of measurements showing strong temperature ($T$) dependence of Hall coefficient ($R_H$) in correlated materials (eg. cuprate superconductors and other oxide materials) and such plots are available in many recent experimental papers. However, I could not find any $R_H$ vs $T$ plot...
45. ### Hall effect -- calculate carrier mobility and density

Homework Statement A metallic film has length L=10mm, width W=1mm and thickness t=1##\mu m##. The current is parallel to the long edge and has magnitude ##I=0.7A##. Longitudinal voltage is ##V=1V## and it doesn't change with magnetic field. The Hall (transverse) voltage ##V_H## increases at...
46. ### Question about a Hall effect sensor

Been thinking to make a quadcopter, not a huge one, a fairly small and light one to start out with. The problem is I would like it to read the RPM of each engine separately. There are several ways I have came up with: - One of them is to use the current reading and calibrate it, however using...
47. ### I How is Fleming's left hand rule applied in Hall effect

I've been reading the explanation of Britannica.com about the direction of magnetic force on a moving charge in hall effect. "Whether the current is a movement of positive particles, negative particles in the opposite direction, or a mixture of the two, a perpendicular magnetic field displaces...
48. ### I Finding mobility constant in the context of the Hall effect

A slab made of unknown material is connected to a power supply as shown in the figure. There is a uniform magnetic field of 0.7 tesla pointing upward throughout this region (perpendicular to the horizontal slab). Two voltmeters are connected to the slab and read steady voltages as shown...
49. ### I Carrier Concentration in a Semiconductor

Suppose I have an n-doped semiconductor and want to measure the electron concentration in the conduction band as a function of temperature. How would I go about doing this by measuring the Hall coefficient as a function of temperature, given that I don't know the electron and hole mobilities...
50. ### Induced EMF from moving conducting rod

Homework Statement Lets say we have two horizontal rails connected by a resistor to the left, and we have a movable conducting rod that slides without friction on the rails.There is a uniform magnetic field going into the page. Homework Equations F = ILB[/B]The Attempt at a Solution Now, I...