Hall Effect Sensor Calculator

Calculate Hall voltage, Hall coefficient, and sensitivity for Hall effect sensors. Useful for magnetic field measurement, current sensing, and position detection.

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Formula

V_H = \frac{R_H \cdot I \cdot B}{t}, \quad R_H = \frac{1}{n \cdot e}

V_H — Hall voltage (V)

R_H — Hall coefficient (m³/C)

I — Control current (A)

B — Magnetic flux density (T)

t — Element thickness (m)

n — Charge carrier density (m⁻³)

e — Elementary charge (1.602×10⁻¹⁹) (C)

How It Works

The Hall Effect describes the generation of a transverse voltage in a conductor or semiconductor when a magnetic field is applied perpendicular to the current flow. This phenomenon occurs due to the Lorentz force deflecting charge carriers, creating a potential difference across the material. The Hall coefficient and resulting Hall voltage provide critical insights into semiconductor properties and magnetic field interactions.

Worked Example

Problem: Calculate the Hall voltage for a semiconductor with the following parameters: carrier density n = 2×10¹⁸ cm⁻³, current I = 0.1 A, magnetic flux density B = 0.5 T, and material thickness t = 2 mm Solution: 1. Calculate Hall coefficient: RH = 1 / (n · e) = 1 / (2×10¹⁸ · 1.602×10⁻¹⁹) = 3.12×10⁻⁷ m³/C 2. Compute Hall voltage: VH = (RH · I · B) / t = (3.12×10⁻⁷ · 0.1 · 0.5) / (0.002) = 0.0078 V or 7.8 mV

Practical Tips

✓Calibrate sensor with known magnetic field strengths
✓Consider temperature coefficients for precise measurements
✓Use high-quality semiconductor materials for consistent results

Common Mistakes

✗Neglecting carrier density variation with temperature
✗Assuming uniform magnetic field across sensor surface
✗Incorrectly converting units of measurement

Frequently Asked Questions

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