Hall Coefficient Calculator

If we apply a voltage difference to a wire, the electric current will start to flow. The charge carriers responsible for electric current will move along straight lines accelerated by the electric field until they collide with each other. You can learn more about this in our acceleration in the electric field calculator. After the collision, they will be again accelerated, resulting in an effective velocity, called the drift velocity, directed along the wire.

Instead of a thin wire, we can imagine a flat, sandwich-like piece of a conductor. Now, besides applying the voltage difference, we also place it in the magnetic field. The magnetic field is in the direction perpendicular to the flat conductor. Due to the Lorentz force, the paths of charge carriers curve, resulting in an accumulation of charge carriers on one side of the conductor. This accumulation leads to a voltage difference V across the conductor. The appearance of the voltage difference due to the magnetic field is the Hall effect.

To learn more about Lorentz force, visit our Lorentz Force Calculator.

The Hall coefficient formula quantifies the strength of the Hall effect. The Hall coefficient is defined as

RH = V × t / (I × B)

where:

• RH [m³/C] — Hall coefficient;
• V [V] — Observed voltage difference;
• t [m] — Thickness of the conductor;
• I [A] — Current running through the conductor; and
• B [T] — Magnetic field.

The Hall coefficient reveals the nature of the charge carriers, their concentration in the conductor, and their charge. The formula is

RH = - 1/(n × q)

where:

• n [1/m³] — Concentration of the carriers; and
• q [C] — Charge of a single carrier.

The Hall effect is significant because it allows us to find out the sign of the charge carriers. For example, with the Hall effect, we can demonstrate that in some semiconductors, the current is carried by positively charged holes and not by electrons.

Interested in learning about the electron concentration in intrinsic semiconductors? Visit our intrinsic carrier concentration calculator.

With the Hall coefficient calculator, you can quickly compute the Hall coefficient. You can also get other quantities from the Hall coefficient formula if you know the Hall coefficient. For example, the Hall effect is sometimes used to measure the magnetic field. It is simple to measure the voltage difference V with a voltmeter and the current I with an ammeter. If we know the Hall coefficient, we can then easily find the magnetic field.

For example, the Hall coefficient of copper is RH = 0.133 mm³/C. Say we have a copper plate of thickness t = 0.02 mm. If we run a current of I = 10 A through it and observe a voltage difference of V = 0.05 mV, we would get that the magnetic field is B = 0.7519 T.