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Hall Voltage Formula
The Hall voltage is calculated from current, magnetic field, mobile charge density, electron charge, and the distance across the conducting material.
V_H = (I*B)/(n*q*d)
- VH = Hall voltage, in volts (V)
- I = current through the material, in amperes (A)
- B = magnetic field strength, in teslas (T)
- n = density of mobile charges, in electrons per cubic meter (electrons/m³)
- q = electron charge, 1.60217662 × 10-19 coulombs (C)
- d = distance or thickness across the material, in meters (m)
If Hall voltage is the missing value, the calculator uses the formula above. If another value is missing, it rearranges the same relationship.
I = (V_H*n*q*d)/B
B = (I*n*q*d)/V_H
n = (I*B)/(V_H*q*d)
d = (I*B)/(V_H*n*q)
- Calculate Hall voltage: enter current, magnetic field, charge density, and distance.
- Calculate current: enter Hall voltage, magnetic field, charge density, and distance.
- Calculate magnetic field: enter Hall voltage, current, charge density, and distance.
- Calculate charge density: enter Hall voltage, current, magnetic field, and distance.
- Calculate distance: enter Hall voltage, current, magnetic field, and charge density.
Hall Voltage Unit Conversions and Typical Inputs
Use these conversions when checking values by hand. The calculator converts inputs to base SI units before applying the formula.
| Quantity | Unit | Base unit conversion |
|---|---|---|
| Current | mA | 1 mA = 0.001 A |
| Current | kA | 1 kA = 1000 A |
| Magnetic field | G | 1 G = 0.0001 T |
| Distance | cm | 1 cm = 0.01 m |
| Distance | mm | 1 mm = 0.001 m |
| Hall voltage | mV | 1 mV = 0.001 V |
Mobile charge density depends strongly on the material. These values are rough reference ranges only.
| Material type | Typical mobile charge density | Notes |
|---|---|---|
| Metals | 1028 to 1029 electrons/m³ | Very high carrier density, usually small Hall voltage |
| Doped semiconductors | 1021 to 1025 electrons/m³ | Lower carrier density, often larger Hall voltage |
| Lightly doped semiconductors | 1016 to 1021 electrons/m³ | Highly sensitive to temperature and doping level |
Hall Voltage Examples
Example 1: Calculate Hall voltage
Suppose the current is 2 A, the magnetic field is 0.5 T, the charge density is 8.5 × 1028 electrons/m³, and the distance is 0.001 m.
V_H = (I*B)/(n*q*d)
V_H = (2*0.5)/(8.5e28*1.60217662e-19*0.001)
V_H = 7.34e-8 V
The Hall voltage is approximately 7.34 × 10-8 V.
Example 2: Calculate charge density
Suppose the current is 0.1 A, the magnetic field is 0.2 T, the Hall voltage is 0.005 V, and the distance is 0.002 m.
n = (I*B)/(V_H*q*d)
n = (0.1*0.2)/(0.005*1.60217662e-19*0.002)
n = 1.248e22 electrons/m^3
The mobile charge density is approximately 1.25 × 1022 electrons/m³.
Hall Voltage FAQ
What is Hall voltage?
Hall voltage is the voltage that appears across a conductor or semiconductor when current flows through it while a magnetic field is applied perpendicular to the current. Moving charges are pushed sideways by the magnetic force, creating a voltage difference across the material.
Why is the electron charge included in the formula?
The Hall effect depends on the force on individual charge carriers. The electron charge converts the number density of mobile charges into charge per unit volume. This calculator uses 1.60217662 × 10-19 C as the magnitude of the electron charge.
Why are Hall voltages often very small?
Hall voltage is inversely proportional to charge density and distance. Metals have very high mobile charge densities, so the Hall voltage is often extremely small. Semiconductors usually have lower carrier densities, so the Hall voltage can be larger for the same current, magnetic field, and thickness.
