Electromagnetism ★★☆ Moderate

🔵 Hall Effect

Current flows through a conductor in a perpendicular magnetic field. The Lorentz force F = qv × B deflects charge carriers, accumulating charge on one face and generating the Hall voltage: VH = IB/(nqd).

VH = 0.00 mV
Drift vd = 0.00 mm/s
FL = 0.00 aN
Type: n-type
VH = IB / (nqd)  │  FL = qvdB  │  RH = 1/(nq)

The Hall Effect (1879)

Discovered by Edwin Hall, this effect arises when current-carrying charge carriers experience a Lorentz force perpendicular to both their velocity and an applied magnetic field. They accumulate on one face of the conductor until the electric force from the built-up charge exactly balances the magnetic force — establishing the Hall voltage.

In n-type semiconductors, electrons (blue) carry current in the −x direction. In p-type, holes (red) carry current in the +x direction. Crucially, the Hall voltage polarity reverses, allowing you to determine the majority carrier type — key in semiconductor characterisation.

About Hall Effect

The Hall effect occurs when a current-carrying conductor is placed in a perpendicular magnetic field: the Lorentz force deflects charge carriers sideways, building up a transverse electric field until it balances the magnetic force. The resulting Hall voltage is VH = IB/(nqt), where n is the carrier density, q the carrier charge, and t the conductor thickness. It is the primary method for determining whether a semiconductor is n-type or p-type and for measuring carrier concentrations — a routine step in fabricating transistors and integrated circuits.

In this simulation you can adjust the current magnitude, applied magnetic field strength, and switch between electron and hole conductors. Watch the carrier deflection build the Hall voltage in real time and observe how the polarity of VH reverses when you flip carrier type.

Frequently Asked Questions

What causes the Hall voltage to appear?

When charge carriers moving along a conductor experience a perpendicular magnetic field, the Lorentz force F = qv×B pushes them to one side of the material. Carriers accumulate on that face, creating a transverse electric field. The Hall voltage builds until the electric force exactly cancels the magnetic force, giving a steady VH = IB/(nqt).

How does the Hall effect distinguish n-type from p-type semiconductors?

In an n-type material the carriers are electrons; in p-type they are positive holes. Because the two carrier types travel in opposite directions under the same applied current, the Lorentz force pushes them to the same face — but the polarity of the resulting Hall voltage is opposite. Measuring the sign of VH therefore unambiguously identifies the majority carrier type.

What is the Hall coefficient and why is it useful?

The Hall coefficient RH = EH/(jB) = 1/(nq) (for a simple single-carrier model) encapsulates how strongly a material responds to the Hall effect. Because it depends on carrier density n, measuring RH gives a direct, non-destructive measure of doping level in a semiconductor without needing to dissolve or contact-etch the sample.

What is the Quantum Hall Effect?

At very low temperatures and high magnetic fields, the Hall resistance of a two-dimensional electron gas becomes quantised in exact integer (or fractional) multiples of h/e² ≈ 25,813 Ω. The integer quantum Hall effect (1980, Klaus von Klitzing, Nobel Prize 1985) is so precise that it now defines the SI ohm. The fractional version arises from correlated electron states and is even more exotic.

How large is a typical Hall voltage in a metal?

Metals have carrier densities of order 10²⁸ m⁻³, so VH is typically only microvolts for practical currents and fields. Semiconductors have much lower carrier densities (10¹⁵–10²³ m⁻³), giving millivolt-range Hall voltages that are far easier to measure — which is why Hall sensors use doped silicon or III-V compounds rather than copper.

What practical devices use the Hall effect?

Hall-effect sensors are found in brushless DC motors (to detect rotor position without mechanical contact), automotive ABS wheel-speed sensors, current clamps (measuring current without breaking the circuit), smartphone compasses, and laboratory gaussmeters. The global Hall sensor market exceeds £3 billion annually.

Does the Hall effect occur in liquids or plasmas?

Yes. In conducting fluids such as molten metals and plasmas, the Hall effect modifies the effective conductivity tensor, introducing off-diagonal terms. In plasmas this leads to the Hall MHD regime important in astrophysics (e.g., protoplanetary disc dynamics) and in Hall thrusters used for satellite propulsion.

How does carrier mobility relate to the Hall angle?

The Hall angle θH = arctan(μB), where μ is carrier mobility (in m²V⁻¹s⁻¹) and B is field strength. In a high-mobility semiconductor like InSb (μ ≈ 8 m²V⁻¹s⁻¹) at 1 T, the Hall angle approaches 83°, meaning almost all current flows transversely — a dramatic deflection compared with copper (μ ≈ 4×10⁻³ m²V⁻¹s⁻¹).

Can the Hall effect measure magnetic field strength?

Yes — Hall probes are standard laboratory instruments for measuring magnetic fields from sub-millitesla to several tesla. A thin semiconductor wafer is biased with a fixed current; the output voltage VH is linearly proportional to B, giving a portable, DC-capable magnetometer with microsecond response time.

What is the anomalous Hall effect?

In ferromagnetic materials an additional transverse voltage appears even without an external field, due to spin-orbit coupling and the internal magnetisation M. The anomalous Hall effect is proportional to M rather than B and is exploited in spintronics research to read magnetic states in memory devices without needing large external fields.

Why is the Hall effect particularly large in thin films?

The Hall voltage VH = IB/(nqt) is inversely proportional to the thickness t of the conductor. Making t very small (nanometre-scale thin films) therefore amplifies VH dramatically for the same current and field, which is why modern Hall sensors use epitaxially grown thin-film structures rather than bulk material.

About this simulation

This simulation visualises the Hall effect: charge carriers drifting through a slab-shaped conductor feel a sideways Lorentz force from a perpendicular magnetic field and pile up on one edge until the resulting transverse electric field balances that force. The equilibrium Hall voltage follows VH = IB/(nqd), where I is the current, B the field, n the carrier density, q the carrier charge and d the slab thickness. Swapping between n-type and p-type carriers flips the sign of VH even though the visible current direction looks similar, which is exactly how real semiconductor labs identify majority carrier type.

🔬 What it shows

Individual electrons (blue, marked −) or holes (red, marked +) drifting along a conductor slab inside a magnetic field shown by ⊙/⊗ symbols. As they deflect sideways, one face of the slab accumulates charge, shown by the coloured top and bottom edges, while a dashed yellow line tracks the live Hall voltage building up between them.

🎮 How to use

Drag the Current I slider (0.5–5 A) and B-field slider (0–3 T) to change the Lorentz force, and the Carrier density n slider (0.1–5 ×10²² per cubic metre) to see how a denser carrier gas reduces VH for the same current and field. Toggle the n-type/p-type buttons to flip carrier sign and watch the Hall voltage polarity reverse, and use Pause/Play to freeze the carriers at any instant.

💡 Did you know?

Edwin Hall discovered this effect in 1879, decades before the electron itself was identified, simply by noticing that a magnetic field could shift the voltage across a current-carrying gold leaf. At extreme low temperatures and high fields, a two-dimensional version of this effect becomes so precisely quantised that it now defines the SI ohm.

Frequently asked questions

What do the Current, B-field and carrier density sliders control?

Current I sets how much charge per second flows through the slab, B-field sets the strength of the perpendicular magnetic field bending the carriers' paths, and carrier density n sets how many charge carriers per cubic metre share that current. All three feed directly into VH = IB/(nqd): raising I or B increases the Hall voltage, while raising n spreads the same current over more carriers and reduces it.

Why does switching from n-type to p-type flip the Hall voltage sign?

Electrons and holes carrying the same conventional current actually drift in opposite physical directions, since electrons are negative. The magnetic force qv×B on an oppositely charged, oppositely moving carrier pushes it toward the same physical edge as before, but the sign of the accumulated charge there is reversed — so the measured VH flips polarity, letting engineers read off the majority carrier type directly from its sign.

Why is the Lorentz force shown in attonewtons?

The force on a single carrier, FL = qvdB, involves the elementary charge q ≈ 1.6×10⁻¹⁹ coulombs and typical drift speeds of only millimetres per second, so the resulting force works out to roughly 10⁻¹⁸ newtons — an attonewton. Displaying such a tiny per-particle force helps make clear just how weak an individual magnetic deflection is, even though millions of carriers acting together produce an easily measured voltage.

What does the drift velocity readout represent?

The drift velocity vd is the average net speed at which carriers move along the slab under the applied current, calculated from I = nqvdA, where A is the slab's cross-sectional area. It is typically only millimetres per second — far slower than the near-instant electrical signal, since that signal propagates as an electromagnetic disturbance rather than as the carriers themselves travelling the circuit.

What happens if you set the current or magnetic field to zero?

With either Current or B-field dragged to its minimum, the Lorentz force term qvdB collapses toward zero, so carriers drift straight along the slab without deflecting and the Hall voltage reading falls to essentially zero. This confirms that the Hall effect is not an intrinsic property of the material alone — it only appears when both a current and a transverse magnetic field are present simultaneously.