The
Contents 1 Discovery 2 Theory 2.1
3 Applications 3.1 Advantages over other methods 3.2 Disadvantages compared with other methods 3.3 Contemporary applications 3.3.1 Ferrite toroid
4 The Corbino effect 5 See also 6 References 7 Sources 8 Further reading 9 External links Discovery[edit]
The
Play media Animation showing the simplified principle For a simple metal where there is only one type of charge carrier (electrons), the Hall voltage VH can be derived by using the Lorentz force and seeing that, in the steady-state condition, charges are not moving in the y-axis direction. Thus, the magnetic force on each electron in the y-axis direction is cancelled by a y-axis electrical force due to the buildup of charges. The vx term is the drift velocity of the current which is assumed at this point to be holes by convention. The vxBz term is negative in the y-axis direction by the right hand rule. F = q ( E + ( v × B ) ) displaystyle mathbf F =q bigl ( mathbf E +(mathbf v times mathbf B ) bigl ) In steady state, F = 0, so 0 = Ey − vxBz, where Ey is assigned in the direction of the y-axis, (and not with the arrow of the induced electric field ξy as in the image (pointing in the −y direction), which tells you where the field caused by the electrons is pointing). In wires, electrons instead of holes are flowing, so vx → −vx and q → −q. Also Ey = −VH/w. Substituting these changes gives V H = v x B z w displaystyle V_ mathrm H =v_ x B_ z w The conventional "hole" current is in the negative direction of the electron current and the negative of the electrical charge which gives Ix = ntw(−vx)(−e) where n is charge carrier density, tw is the cross-sectional area, and −e is the charge of each electron. Solving for w displaystyle w and plugging into the above gives the Hall voltage: V H = I x B z n t e displaystyle V_ mathrm H = frac I_ x B_ z nte If the charge build up had been positive (as it appears in some semiconductors), then the VH assigned in the image would have been negative (positive charge would have built up on the left side). The Hall coefficient is defined as R H = E y j x B z displaystyle R_ mathrm H = frac E_ y j_ x B_ z where j is the current density of the carrier electrons, and Ey is the induced electric field. In SI units, this becomes R H = E y j x B = V H t I B = − 1 n e . displaystyle R_ mathrm H = frac E_ y j_ x B = frac V_ mathrm H t IB =- frac 1 ne . (The units of RH are usually expressed as m3/C, or Ω·cm/G, or other
variants.) As a result, the
R H = p μ h 2 − n μ e 2 e ( p μ h + n μ e ) 2 displaystyle R_ mathrm H = frac pmu _ mathrm h ^ 2 -nmu _ mathrm e ^ 2 eleft(pmu _ mathrm h +nmu _ mathrm e right)^ 2 or equivalently R H = ( p − n b 2 ) e ( p + n b ) 2 displaystyle R_ mathrm H = frac left(p-nb^ 2 right) eleft(p+nbright)^ 2 with b = μ e μ h displaystyle b= frac mu _ mathrm e mu _ mathrm h . Here n is the electron concentration, p the hole concentration, μe
the electron mobility, μh the hole mobility and e the elementary
charge.
For large applied fields the simpler expression analogous to that for
a single carrier type holds.
Relationship with star formation[edit]
Although it is well known that magnetic fields play an important role
in star formation, research models[9][10][11] indicate that Hall
diffusion critically influences the dynamics of gravitational collapse
that forms protostars.
Quantum Hall effect[edit]
Main article: Quantum Hall effect
For a two-dimensional electron system which can be produced in a
MOSFET, in the presence of large magnetic field strength and low
temperature, one can observe the quantum Hall effect, in which the
Hall conductance σ undergoes quantum Hall transitions to take on the
quantized values.
Spin Hall effect[edit]
Main article: Spin Hall effect
The spin
β = Ω e ν = e B m e ν displaystyle beta = frac Omega _ mathrm e nu = frac eB m_ mathrm e nu where e is the elementary charge (approximately 6981160000000000000♠1.6×10−19 C) B is the magnetic field (in teslas) me is the electron mass (approximately 6969910000000000000♠9.1×10−31 kg). The Hall parameter value increases with the magnetic field strength. Physically, the trajectories of electrons are curved by the Lorentz force. Nevertheless, when the Hall parameter is low, their motion between two encounters with heavy particles (neutral or ion) is almost linear. But if the Hall parameter is high, the electron movements are highly curved. The current density vector, J, is no longer collinear with the electric field vector, E. The two vectors J and E make the Hall angle, θ, which also gives the Hall parameter: β = tan ( θ ) . displaystyle beta =tan(theta ). Applications[edit]
Hall probes are often used as magnetometers, i.e. to measure magnetic
fields, or inspect materials (such as tubing or pipelines) using the
principles of magnetic flux leakage.
When electrons flow through a conductor, a magnetic field is produced.
Thus, it is possible to create a non-contacting current sensor. The
device has three terminals. A sensor voltage is applied across two
terminals and the third provides a voltage proportional to the current
being sensed. This has several advantages; no additional resistance (a
shunt, required for the most common current sensing method) need be
inserted in the primary circuit. Also, the voltage present on the line
to be sensed is not transmitted to the sensor, which enhances the
safety of measuring equipment.
Disadvantages compared with other methods[edit]
Diagram of
Hall sensors can detect stray magnetic fields easily, including that of Earth, so they work well as electronic compasses: but this also means that such stray fields can hinder accurate measurements of small magnetic fields. To solve this problem, Hall sensors are often integrated with magnetic shielding of some kind. For example, a Hall sensor integrated into a ferrite ring (as shown) can reduce the detection of stray fields by a factor of 100 or better (as the external magnetic fields cancel across the ring, giving no residual magnetic flux). This configuration also provides an improvement in signal-to-noise ratio and drift effects of over 20 times that of a bare Hall device. The range of a given feedthrough sensor may be extended upward and downward by appropriate wiring. To extend the range to lower currents, multiple turns of the current-carrying wire may be made through the opening, each turn adding to the sensor output the same quantity; when the sensor is installed onto a printed circuit board, the turns can be carried out by a staple on the board. To extend the range to higher currents, a current divider may be used. The divider splits the current across two wires of differing widths and the thinner wire, carrying a smaller proportion of the total current, passes through the sensor. Multiple 'turns' and corresponding transfer function. Split ring clamp-on sensor[edit]
A variation on the ring sensor uses a split sensor which is clamped
onto the line enabling the device to be used in temporary test
equipment. If used in a permanent installation, a split sensor allows
the electric current to be tested without dismantling the existing
circuit.
Analog multiplication[edit]
The output is proportional to both the applied magnetic field and the
applied sensor voltage. If the magnetic field is applied by a
solenoid, the sensor output is proportional to the product of the
current through the solenoid and the sensor voltage. As most
applications requiring computation are now performed by small digital
computers, the remaining useful application is in power sensing, which
combines current sensing with voltage sensing in a single Hall effect
device.
Power measurement[edit]
By sensing the current provided to a load and using the device's
applied voltage as a sensor voltage it is possible to determine the
power dissipated by a device.
Position and motion sensing[edit]
Corbino disc – dashed curves represent logarithmic spiral paths of deflected electrons The Corbino effect is a phenomenon involving the Hall effect, but a disc-shaped metal sample is used in place of a rectangular one. Because of its shape the Corbino disc allows the observation of Hall effect–based magnetoresistance without the associated Hall voltage. A radial current through a circular disc, subjected to a magnetic field perpendicular to the plane of the disc, produces a "circular" current through the disc.[14] The absence of the free transverse boundaries renders the interpretation of the Corbino effect simpler than that of the Hall effect. See also[edit] Electronics portal Capacitor
Transducer
References[edit] ^
Sources[edit] Introduction to Plasma Physics and Controlled Fusion, Volume 1, Plasma Physics, Second Edition, 1984, Francis F. Chen Further reading[edit] Classical
External links[edit] Patents U.S. Patent 1,778,796, P. H. Craig, System and apparatus employing the Hall effect U.S. Patent 3,596,114, J. T. Maupin, E. A. Vorthmann, Hall effect contactless switch with prebiased Schmitt trigger General Understanding and Applying the Hall Effect
Hall Effect Thrusters Alta Space
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