What is the Hall effect?
The Hall effect is a physical phenomenon where a voltage difference — the Hall voltage — develops across a conductor when an electric current flows through it and a magnetic field is applied perpendicular to the current. The magnetic Lorentz force deflects charge carriers to one side, creating a transverse electric field. It was discovered by Edwin Hall in 1879. See also our Coulomb's Law Calculator.
What does the Hall coefficient tell you?
The Hall coefficient (R_H) reveals the sign and concentration of charge carriers in a material. A negative R_H indicates electrons (n-type) are the majority carriers, while a positive R_H indicates holes (p-type). Its magnitude is inversely proportional to carrier concentration — larger absolute values mean fewer carriers.
What is the Hall coefficient formula?
The Hall coefficient is calculated as R_H = (V_H × t) / (I × B), where V_H is the Hall voltage, t is the sample thickness, I is the applied current, and B is the magnetic flux density. It can also be expressed as R_H = −1 / (n × q), where n is carrier concentration and q is carrier charge.
What are the units of the Hall coefficient?
The SI unit of the Hall coefficient is cubic metres per coulomb (m³/C). It is sometimes also expressed in cm³/C or mm³/C depending on the scale of the measurement. In the formula R_H = V × t / (I × B), combining volts, metres, amperes, and tesla gives m³/C.
How do I determine carrier concentration from the Hall coefficient?
Carrier concentration n = 1 / |R_H × q|, where q is the elementary charge (1.602 × 10⁻¹⁹ C). This gives the number of charge carriers per cubic metre. A smaller Hall coefficient magnitude corresponds to a higher carrier density, which is typical in metals compared to semiconductors.
Why is my Hall coefficient negative?
A negative Hall coefficient means the dominant charge carriers in your material are electrons (n-type). Since electrons carry negative charge, the sign convention in the Hall formula yields a negative value. Positive values indicate hole conduction (p-type), common in many semiconductors like p-doped silicon or germanium.
What is the difference between Hall voltage and Hall coefficient?
Hall voltage (V_H) is the measurable transverse voltage that appears across the sample during the experiment — it depends on current, field strength, and sample geometry. The Hall coefficient (R_H) is a material property derived from V_H; it is independent of sample dimensions and characterises the conductor's carrier type and density.
Can the Hall effect be used to measure magnetic fields?
Yes — Hall effect sensors are widely used to measure magnetic field strength. If R_H and the sample dimensions are known, rearranging the formula gives B = (V_H × t) / (R_H × I). This principle underlies Hall probes used in scientific instruments, electric motors, and proximity sensors. You might also find our find Induced EMF (ε) with Lenz's Law Calculator useful.