The Hall effect occurs when a current carrying conductor or semiconductor is placed in a magnetic field and a voltage appears across its sides. This sideways voltage reveals that moving charges feel a magnetic force perpendicular to both their motion and the magnetic field. The effect matters because it gives direct evidence that electric current is carried by charged particles.
It is also a practical way to measure magnetic fields, current, and even the type and density of charge carriers in a material.
Inside the slab, charge carriers drift along the direction of current while the magnetic field points through the material. The magnetic force pushes the carriers sideways until separated charge builds an electric field that balances the magnetic force. This balance creates the Hall voltage, which can be measured between two side contacts.
In semiconductors, the sign and size of the Hall voltage help identify whether electrons or holes are the main carriers.
Understanding Physics: The Hall Effect
A useful detail is that a magnetic field changes the direction of a moving charge without directly changing its speed. The force acts at right angles to the charge motion. This is why the charge path bends sideways rather than speeding up or slowing down.
Direction matters greatly. For a positive carrier, use the right hand rule for conventional current and magnetic field direction. Electrons have negative charge, so their deflection is opposite.
The side that becomes negative or positive is therefore a clue about the carriers inside the material. This sign test was especially important because it showed that current in different materials is not always carried in the same way.
The Hall voltage settles at a particular value because charge separation cannot grow forever. As charges collect at one edge, they create an electric field across the sample. That electric field pushes later charges back in the opposite direction.
Equilibrium is reached when the electric push matches the magnetic push. The result depends on how fast the carriers drift, not on their random thermal motion. In a metal, electrons move randomly at high speeds, but those random directions cancel out.
Their tiny average drift caused by the current is what produces the Hall effect. A larger current gives a larger Hall voltage because it means more charge passes through each second.
Material thickness has a strong effect. A thin sample can produce a much larger Hall voltage than a thick sample carrying the same current. This happens because the current is shared among fewer charge carriers across the thinner cross section.
Materials with a low carrier density give especially clear Hall signals. Semiconductors are useful for this reason. Their carrier density can change with temperature, light, or added impurities.
Engineers use Hall measurements to study these changes. A Hall probe can measure magnetic field strength near a motor, a loudspeaker magnet, or an electric current cable.
Many phones use Hall sensors to detect a magnetic cover. Cars use them to track wheel rotation or the position of moving parts.
When learning this topic, keep the directions separate. Current direction is defined as the direction positive charge would move. Electron drift goes the other way in most metal wires.
The magnetic field direction is often shown by dots for a field coming out of the page and crosses for a field going into the page. Draw the sample as a rectangle, label the current, field, sideways force, and charge buildup before choosing a rule. Check the units too.
Hall voltage is measured in volts, magnetic field in tesla, and carrier density as the number of carriers per cubic metre. Real measurements can be affected by poor electrical contacts, uneven sample thickness, heating, or extra voltages caused by the measuring circuit. Good experiments reverse the magnetic field or current and compare the readings, since the true Hall voltage reverses sign.
Key Facts
- Magnetic force on a moving charge: F = qvB sin(theta)
- For the Hall effect with v perpendicular to B: F = qv_dB
- At equilibrium, electric and magnetic forces balance: qE_H = qv_dB
- Hall field: E_H = v_dB
- Hall voltage across width w: V_H = E_Hw = v_dBw
- For a slab of thickness t carrying current I: V_H = IB/(nqt)
Vocabulary
- Hall effect
- The Hall effect is the production of a voltage across a current carrying material when it is placed in a magnetic field perpendicular to the current.
- Hall voltage
- Hall voltage is the transverse voltage caused by the sideways separation of charge carriers in a magnetic field.
- Charge carrier
- A charge carrier is a mobile charged particle, such as an electron or a hole, that transports electric current through a material.
- Drift velocity
- Drift velocity is the average speed of charge carriers through a material due to an applied electric field.
- Carrier density
- Carrier density is the number of mobile charge carriers per unit volume of a material.
Common Mistakes to Avoid
- Using the current direction as the electron motion direction is wrong because conventional current points opposite to electron drift in metals and n type semiconductors.
- Forgetting that the Hall voltage is transverse is wrong because it is measured across the width of the slab, not along the direction of the main current.
- Ignoring the sign of the charge carrier is wrong because electrons and holes deflect in opposite ways and produce Hall voltages of opposite polarity.
- Assuming the Hall voltage grows with thickness is wrong because V_H = IB/(nqt), so a thicker slab gives a smaller Hall voltage for the same current and magnetic field.
Practice Questions
- 1 A Hall sensor carries a current of 0.20 A through a slab with thickness 1.0 mm. The carrier density is 8.5 x 10^28 m^-3 and the charge magnitude is 1.60 x 10^-19 C. If the magnetic field is 0.50 T, calculate the Hall voltage.
- 2 A semiconductor Hall probe has carrier density 2.0 x 10^22 m^-3, thickness 0.50 mm, and current 0.010 A. It measures a Hall voltage of 6.25 mV. Find the magnetic field strength.
- 3 A Hall voltage reverses sign when a sample is replaced by another material under the same current and magnetic field directions. Explain what this indicates about the dominant charge carriers in the two materials.