Name: hall voltage and charge carriers
Uploaded: 2025-05-22T09:05:51.000Z
Duration: 1 min 30 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

motion-and-stability-forces-and-interactions

Motion and Stability- Forces and Interactions

PS.PSc.6.4

The Hall Effect

電荷キャリアとして電子を持つ長方形の電流を運ぶ導体を考えてみましょう。導体の平面に対して垂直に磁場を印加すると、偏向磁力により直線的に移動する電子がドリフトします。
電子は導体の片側に蓄積し、反対側に過剰な正電荷を残します。この電荷分離により、導体内に電界が発生し、磁力に対抗する各電子に電気力がかかります。
平衡状態では、電気力の大きさが磁力と釣り合い、電子のさらなる漂流を止めます。導体の両側の電位差がホール電圧です。
ドリフト速度を電流で表すことにより、ホール電圧を使用して電荷キャリアの数密度を測定することもできます。
ホールプローブは、ホール電圧と導体の既知のパラメータから未知の磁場の大きさを測定します。
この発見の重要な応用は、ホール電圧の極性が導体内の電荷キャリアが負か正かを意味することです。

<ol>
	<li>OpenStaxです。(2019). 大学物理学 Vol.2.【Web版】。514-516から取得 <a href="https://openstax.org/books/university-physics-volume-2/pages/11-6-the-hall-effect">https://openstax.org/books/university-physics-volume-2/pages/11-6-the-hall-effect</a></li>
</ol>

ホール効果

エドウィン H. ホールは 1879 年に、導電性材料内の主な電荷キャリアの極性を識別するために使用できる実験を考案しました。 歴史的な観点から見ると、この実験は、ほとんどの金属の電荷キャリアが負であることを初めて実証したものでした。

<img alt="Figure1" src="/files/ftp_upload/13772/13772_Figure_1.png" style="text-align: center" />

一定の磁場にある幅 L の金属スラブを考えてみましょう。 電子は右から左に移動するため、電子が受ける磁力によって電子はスラブの上端に押し出されます。 これにより、スラブの上端に過剰な負電荷が残り、スラブの下端に過剰な正電荷が残り、その結果、下から上に向かう電界が生じます。 平衡状態が確立されるまで、両端の電荷集中が増加します。 平衡状態では、電子にかかる一方向の電気力は、反対方向の磁力によって釣り合います。 電場と磁場が互いに直交するこのシナリオは、交差磁場状況と呼ばれます。

スラブ内の電流 I は、ドリフト速度 vd とスラブの断面積で表すことができます。 スラブ、A。 ストリップのエッジ間の電位差 (ホール電圧とも呼ばれます) は、次の式で与えられます。

<img alt="Equation1" src="/files/ftp_upload/13772/13772_Equation_1.png" style="text-align: center; height: 40px;" />

ホール電圧の極性は、電荷キャリアが正か負かを示します。 この効果のもう 1 つの重要な用途は、電荷キャリアの密度が既知である材料に対するものです。 測定されたホール電圧は、未知の磁場の値を与える可能性があります。 精密な測定に使用される電磁石の磁界が非常に安定している必要がある研究室では、「ホールプローブ」が使用されます。 場を調整するための電子回路の一部として一般的に使用されます。

エドウィンH.ホールは、1879年に、導電体で優勢な電荷キャリアの極性を特定するために使用できる実験を考案しました...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

Magnetic Forces and Fields

磁力と磁場

KEY TERMS AND CONCEPTS

主要用語と概念

hall voltage and charge carriers

Hall voltage and charge carriers are explained through Edwin H. Hall’s 1879 experiment. His setup helped identify the polarity of the main charge carriers in a conducting material. It also showed, for the first time, that the charge carriers in most metals are negative.

A metal slab is placed in a constant magnetic field. The electrons move from right to left, so the magnetic force pushes them toward the top edge of the slab. This leaves excess negative charge at the top and excess positive charge at the bottom. As a result, an electric field forms from the bottom edge to the top edge.

The charge buildup continues until equilibrium is reached. At that point, the electric force on the electrons balances the magnetic force in the opposite direction. This is called a crossed-field situation because the electric and magnetic fields are perpendicular to each other. The current in the slab, I, can be written in terms of the drift velocity, v d, and the cross-sectional area, A.

The potential difference between the two edges is called the Hall voltage. Its polarity reveals whether the charge carriers are positive or negative. When the density of charge carriers is known, the Hall voltage can also be used to find an unknown magnetic field. In research labs, a Hall probe is often used in electronic circuits to help regulate electromagnet fields so they stay steady for precise measurements.

Hall Voltage and Charge Carriers

magnetism

Magnetic Poles and Everyday Uses

Magnetism appears in many everyday objects, from toys and hangers to elevators, doorbells, and computer devices. Magnets have two poles, called north and south. Like poles repel each other, while unlike poles attract. Both poles can also attract unmagnetized iron. A single magnetic pole cannot be isolated, because every part of a magnet contains both a north pole and a south pole. A compass needle is a simple example of a magnet. It is a thin bar magnet suspended at its center, so it can turn...

magnetic fields

Magnetic Force on Moving Charges

Magnetic force on moving charges depends on motion, charge, and field direction. A moving charge or a current creates a magnetic field in the space around it, along with its electric field. That magnetic field can then push on other moving charges or currents in the field. A magnetic field is a vector field, so it has direction as well as strength. At any point, the field direction is the direction a compass needle’s north pole points. The field strength is defined from the force a charged...

magnetic field lines

Reading Magnetic Field Lines

Magnetic field lines show the direction and strength of a magnetic field. They make it easier to picture how a magnet acts in space. Each line forms a closed loop around the magnet. For a bar magnet, the field lines leave the north pole and curve around to the south pole. They then continue through the magnet back to the north pole. This loop has no beginning or end. Magnetic field lines follow clear rules. The magnetic field points tangent to a field line at any point. A small compass points...

magnetic flux

Magnetic Flux Through Surfaces

Magnetic flux through a surface describes how much magnetic field passes across that surface. It is measured in weber (Wb), the SI unit for magnetic flux. Magnetic flux is a scalar quantity, not a vector. Three factors shape magnetic flux. They are the magnetic field strength B, the area the field crosses, and the orientation of the field relative to the surface. For a small area element dA, the flux depends on the part of the magnetic field that is normal, or perpendicular, to that element at...

motion of a charged particle in a magnetic field

motion-of-a-charged-particle-in-a-magnetic-field

Charged Particle Paths in Magnetic Fields

A charged particle in a magnetic field follows a path that depends on the direction of its velocity. When the field is uniform and the particle moves perpendicular to it, the magnetic field is the main factor that controls the motion, especially in a vacuum. The magnetic force is always perpendicular to the direction of motion, so the particle curves into a circle. Because the force stays perpendicular to velocity, it does no work on the particle. The kinetic energy and speed stay constant...

magnetic force

Magnetic Fields and Moving Charges

Magnetic fields and moving charges create magnetic force. A moving electric charge, or a current made of many moving charges, produces a magnetic field. When another current or moving charge enters that field, it feels a magnetic force in response. At the atomic level, magnetic forces come from interactions between moving electrons in the atoms of two bodies. The strength of magnetic force depends on several factors. It increases with the size of the charge and with the strength of the...

magnetic force on a current-carrying conductor

magnetic-force-on-a-current-carrying-conductor

Current and Magnetic Field Around a Wire

A current-carrying wire creates a magnetic field around it, and moving charges feel a force in that field. Because the magnetic field produced by moving charges is proportional to current, the wire itself acts as a source of magnetic field. A compass placed near the wire shows this effect by lining up tangentially around the wire. The magnetic field around a straight wire forms concentric circular loops. The right-hand rule helps determine the direction of those loops. If the thumb points in...

magnetic force on current-carrying wires: example

magnetic-force-on-current-carrying-wires-example

Balancing Weight with Magnetic Force

Magnetic force can balance the weight of a current-carrying wire when the wire sits in a magnetic field. Moving charges in the wire feel a force, so the wire itself can be pushed upward or downward. This example uses a flexible wire that is 40 cm long and has a mass of 10 g. It is held in a horizontal position inside a constant 0.40 T magnetic field. The goal is to find the current needed to remove the tension in the supporting leads. To do that, a free-body diagram is drawn first. The diagram...

force on a current loop in a magnetic field

force-on-a-current-loop-in-a-magnetic-field

Current Loops and Torque in Motors

Current loops in a magnetic field create the torque that drives a DC motor. A DC motor converts electrical energy into mechanical work. In a motor, wire loops sit inside a magnetic field. When current flows through the loops, the magnetic field pushes on them and makes the shaft rotate. The current is reversed when the loop lines up with the magnetic field. This keeps the torque on the loop going in the same direction. A commutator and brushes handle this reversal. The commutator switches the...

torque on a current loop in a magnetic field

torque-on-a-current-loop-in-a-magnetic-field

Current Loop Torque in Electric Motors

Current loop torque in electric motors shows how magnetic force can make a wire loop rotate. In an electric motor, loops of wire sit between magnets in a magnetic field. When current flows through the loops, the field applies torque. This rotation turns a shaft and converts electrical energy into mechanical energy. A rectangular current-carrying loop with N turns in a uniform magnetic field has zero net force. Even so, it can still experience net torque. The torque depends on the current I,...

the hall effect

Hall voltage and charge carriers are explained through Edwin H. Hall’s 1879 experiment. His setup helped identify the polarity of the main charge carriers in a conducting material. It also showed, for the first time, that the charge carriers in most metals are negative. A metal slab is placed in a constant magnetic field. The electrons move from right to left, so the magnetic force pushes them toward the top edge of the slab. This leaves excess negative charge at the top and excess positive...

thomson's e/m experiment

Electron Speed Selector in Thomson’s Tube

A velocity selector uses electric and magnetic fields to choose charged particles with one speed from a beam. Many beams from a heated cathode contain particles moving at different speeds, so this setup helps produce a uniform beam. The electric and magnetic fields are perpendicular to the particle’s motion and to each other. In this arrangement, a particle with charge q, speed v, and mass m enters from the top. The magnetic field points into the plane of the paper, and the electric field...

key terms and concepts

Learn how Hall voltage forms in a magnetic field, how it reveals charge carrier polarity, and how Hall probes help measure and control magnetic fields.

Hall Voltage and Charge Carriers | JoVE K12

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

Virginia  Standards of Learning

HIgh School

PS.9

PS.9.d

Alabama Course of Study Science

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

9-12.PS.2.3.b

Position and Displacement

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Instantaneous Velocity - I

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Instantaneous Velocity - II

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Average Acceleration

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Instantaneous Acceleration

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Position and Displacement Vectors

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average-and-instantaneous-velocity-vectors

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Acceleration Vectors

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PS.PSc.4.1

Electrical Current

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Drift Velocity

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Current Density

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Resistivity

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Resistance

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Ohm's Law

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Non-ohmic Devices

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Construct an explanation to compare simple series and parallel circuits in terms of Ohm's Law.

PS.PSc.6.2

Continuity Equation

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Boundary Conditions for Current Density

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Electrical Conductivity

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Theory of Metallic Conduction

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PS.PSc.6.3

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Magnetic Force

In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a ...

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Torque On A Current Loop In A Magnetic Field

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magnetic-force-between-two-parallel-currents

Magnetic Force Between Two Parallel Currents

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Magnetic Field Of A Current Loop

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A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field due to a solenoid is ...

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Lenz's Law

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PS.PSc.6.5

Analyze motion in terms of speed, velocity, acceleration, and momentum.

Hall Voltage and Charge Carriers

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