Hall Effect Calculator

The Hall effect occurs when a current-carrying conductor is placed in a magnetic field perpendicular to current flow. The Lorentz force pushes carriers sideways, creating a transverse voltage.

⚡ Electromagnetism📐 Vᴴ = IB/nqt🧪 Semiconductors

Current I (A)

B Field (T)

Carrier density n (m⁻³)

Thickness t (m)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Hall Voltage	V_H	V_H = IB/(nqt)	V
Current	I	—	A
B Field	B	—	T
Carrier Density	n	—	m⁻³
Thickness	t	Thickness in B direction	m

Step-by-Step Examples

Example 1

Copper Hall Voltage

I=10 A, B=1 T, n=8.5e28 m^-3 (copper), t=1 mm.

V_H = 10*1/(8.5e28*1.6e-19*0.001)
V_H = 10/(1.36e7) = 7.35e-7 V = 0.735 uV

✓ Tiny voltage in metals — carrier density very high

Example 2

Silicon Sensor

I=1 mA, B=0.1 T, n=1e16 m^-3, t=0.5 mm.

V_H = 0.001*0.1/(1e16*1.6e-19*0.0005)
V_H = 1e-4/8e-7 = 125 mV

✓ 125 mV — semiconductors give much larger Hall voltage

Example 3

Find Carrier Density

V_H=50 mV, I=5 mA, B=0.3 T, t=0.2 mm.

n = IB/(q*t*V_H) = 0.005*0.3/(1.6e-19*0.0002*0.05)
n = 1.5e-3/1.6e-24 = 9.375e20 m^-3

✓ Carrier density = 9.375e20 per m^3

Real-World Applications

🧲

Magnetic Sensors

Hall sensors in smartphones, cars, and industrial systems measure magnetic field strength.

🚗

ABS Brakes

Hall sensors detect wheel rotation speed for antilock braking systems.

🧪

Semiconductor Physics

Hall measurements characterize carrier type (n or p), density, and mobility.

⚡

Current Sensing

Hall current sensors measure large currents without electrical contact.

Common Mistakes to Avoid

⚠️

Sign tells carrier type

Positive V_H for p-type, negative for n-type semiconductor. Sign identifies which carrier dominates.

⚠️

Metals have tiny Hall voltage

High carrier density (n~10^28) in metals gives very small V_H. Semiconductors (n~10^16) give much larger Hall voltages.

⚠️

Perpendicular geometry required

B must be perpendicular to current I and both perpendicular to measured voltage direction.

Frequently Asked Questions

What determines the sign of Hall voltage? ▾

Sign depends on carrier type. Electrons and holes deflect the same direction by Lorentz force but carry opposite charges, giving opposite Hall voltages.

What is the Hall coefficient? ▾

R_H = 1/(n*q) for single carrier type (m^3/C). Positive for p-type, negative for n-type semiconductors.

How is Hall effect used in current sensors? ▾

A current-carrying conductor placed in a known B field produces V_H proportional to current. Non-contact current measurement.

What is quantum Hall effect? ▾

At very low temperatures and high B fields, Hall resistance takes exact quantized values h/(n*e^2). Used for resistance metrology standard.

How does Hall mobility work? ▾

mu = |R_H| * sigma, where sigma is conductivity. Hall mobility characterizes how easily carriers move in the semiconductor.

Related Physics Calculators

Formula Explorer connections

Interpretation: This relationship connects magnetic fields, moving charge, flux, induction or electromagnetic material response. Assumption: Specify field direction and sign convention. Uniform fields, linear materials, negligible edge effects or sinusoidal steady state may be assumed.

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