The Hall effect describes how charge carriers in a current-carrying material respond to a magnetic field. Measuring the resulting voltage can reveal whether the predominant carriers are negative or positive—a discovery first demonstrated by Edwin Hall in 1879.
Consider a metallic strip carrying current while a magnetic field is applied perpendicular to the motion of its charge carriers. For a strip in which electrons drift from left to right, the magnetic force pushes the electrons toward one edge. The resulting separation of charge leaves one edge negative and the opposite edge positive.
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What is the Hall effect?
It is the development of a transverse voltage across a current-carrying material when a magnetic field deflects its moving charge carriers and separates charge.
What condition marks equilibrium in the Hall effect?
The electric force balances the magnetic force in the opposite direction. In magnitude, eE=evdB, so E=vdB.
What is the Hall-voltage magnitude for a strip?
For carrier density n, current I, field B, strip width l, and current-perpendicular cross-sectional area A,∣VH∣=IBl/(neA).
How does Hall voltage identify the sign of majority carriers?
With the current direction, magnetic field, and sample orientation fixed, opposite carrier signs produce opposite Hall-voltage polarities.
What is a Hall probe used for?
A Hall probe measures a magnetic field from the Hall voltage produced in a sample whose carrier properties and dimensions are known.
Quiz questions
What causes charge carriers to accumulate at opposite edges of a current-carrying strip in a magnetic field?Answer: The magnetic force deflects moving carriers toward one edge, separating charge.
What speed allows a charged particle to pass undeflected through crossed electric and magnetic fields whose forces oppose?Answer: v=BE
An electric field is removed from a charged particle moving perpendicular to a uniform magnetic field. What path does the particle follow?Answer: A circular path, because the magnetic force remains perpendicular to its velocity.
For fixed current, sample geometry, and carrier density, what happens to Hall-voltage magnitude if magnetic-field magnitude doubles?Answer: The Hall-voltage magnitude doubles.
With current, magnetic field, and sample orientation fixed, how can Hall voltage distinguish opposite majority-carrier signs?Answer: Opposite carrier signs produce opposite Hall-voltage polarities.
Based on University Physics Volume 2 by Samuel J. Ling, William Moebs, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.