Welcome to the Hall Voltage Calculator! This tool is designed to help you quickly determine the Hall voltage generated in a material when subjected to a magnetic field. By entering a few key values, you can instantly compute the result, saving time and avoiding manual calculations.
The calculator is simple to use—just provide the current, magnetic field strength, charge carrier density, and material thickness. You can start using it right away, or keep reading to better understand the formula, input parameters, and see a worked-out example.
Understanding the Formula
The primary formula for Hall voltage is:
Vh = (I * B) / (n * e * d)
Where:
- Vh = Hall Voltage
- I = Current
- B = Magnetic Field Strength
- n = Charge Carrier Density
- e = Elementary Charge (1.602 × 10⁻¹⁹ C)
- d = Thickness of the material
An alternative way to express the Hall voltage is:
Vh = (RH * I * B) / d
Where RH is the Hall Coefficient, defined as:
RH = 1 / (n * e)
In simple terms, the Hall voltage depends on how much current is flowing, how strong the magnetic field is, how many charge carriers exist in the material, and how thick the material is. This effect is widely used in physics and electronics for measuring magnetic fields and studying material properties.
Parameters Explained
Current (I): The flow of electric charge through the material, usually measured in amperes (A). Higher current increases the Hall voltage.
Magnetic Field Strength (B): The intensity of the magnetic field applied perpendicular to the current, measured in teslas (T). Stronger fields result in larger Hall voltages.
Charge Carrier Density (n): The number of charge carriers (such as electrons or holes) per cubic meter. Materials with high carrier density produce smaller Hall voltages.
Elementary Charge (e): A constant value of 1.602 × 10⁻¹⁹ coulombs. It represents the charge of a single electron.
Thickness (d): The thickness of the conducting material, measured in meters (m). Thicker samples reduce the measured Hall voltage.
Hall Coefficient (RH): A property of the material that relates its charge carrier density to the Hall effect.
How to Use the Hall Voltage Calculator — Step-by-Step Example
Let’s go through an example calculation:
- Suppose a conductor carries a current of 3 A.
- The applied magnetic field strength is 0.5 T.
- The charge carrier density is 8 × 10²⁸ m⁻³.
- The thickness of the material is 0.002 m.
Using the formula:
Vh = (I * B) / (n * e * d)
Vh = (3 × 0.5) / (8 × 10²⁸ × 1.602 × 10⁻¹⁹ × 0.002)
Vh ≈ 5.85 × 10⁻¹¹ V
So, the Hall voltage in this case is extremely small—on the order of nanovolts. This demonstrates why precise instruments are required to measure the Hall effect in practice.
Additional Information
Here’s a quick reference for constants and values often used in Hall voltage calculations:
| Parameter | Symbol | Typical Value/Unit |
|---|---|---|
| Elementary charge | e | 1.602 × 10⁻¹⁹ C |
| Magnetic field strength | B | Tesla (T) |
| Current | I | Amperes (A) |
| Thickness | d | Meters (m) |
| Charge carrier density | n | 10²² – 10²⁹ m⁻³ |
FAQs
The Hall effect is commonly used in sensors to measure magnetic field strength, determine carrier type (electron or hole), and study material properties.
Because charge carrier densities in conductors and semiconductors are very high, the resulting Hall voltage tends to be in the microvolt or nanovolt range.
Yes. The sign of the Hall coefficient indicates whether the material’s dominant charge carriers are electrons (negative) or holes (positive).