Name: electron drift in metallic conduction
Uploaded: 2023-09-18T17:11:19.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

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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.6.3

Theory of Metallic Conduction

Kiedy pole elektryczne jest przyłożone do przewodnika, wolne elektrony dryfują w kierunku przeciwnym do kierunku pola, zderzając się z jonami kryształu.
Gdyby zastosowane pole było równe zero, ruch losowy spowodowałby średnio zerowy dryf netto, ponieważ zderzenia losowo zmieniałyby swoje kierunki. Średni czas między kolizjami nazywany jest średnim czasem wolnym.
Przyspieszenie elektronu jest określone przez siłę elektryczną działającą na masę. Jego prędkość w dowolnym momencie jest wyrażona przez prędkość początkową, przyspieszenie i czas.
Uśrednienie obu stron nad zderzeniami daje średnią prędkość. Ponieważ jednak średni dryft spowodowany zderzeniami wynosi zero, prędkość dryfu jest określona przez iloczyn przyspieszenia i średniego czasu wolnego.
Wykorzystując zależność między gęstością prądu a prędkością dryfu, gęstość prądu jest związana z polem elektrycznym, co jest prawem Ohma.
Tak więc przewodność elektryczna jest wyrażona przez liczbę wolnych elektronów na jednostkę objętości, ładunek i masę elektronu oraz średni czas wolny.

<ol>
	<li>Young, H.D. i Freedman, R.A. (2012). Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson; sekcja 25.6; strony 838–839.</li>
	<li>Griffiths, David J. (1999). Wprowadzenie do elektrodynamiki (wyd. 3). Górna rzeka Saddle, New Jersey 07458; ppkt 7.1.1; strony 289–290.</li>
</ol>

teoria przewodnictwa metalicznego

Przewodnictwo wolnych elektronów w przewodniku najlepiej opisuje mechanika kwantowa. Jednak model klasyczny pozwala na przewidywania zbliżone do wyników mechaniki kwantowej. Nazywa się to teorią przewodnictwa metalicznego.

W tej teorii druga zasada dynamiki Newtona służy do określenia przyspieszenia elektronu w obecności przyłożonego pola elektrycznego. Następnie jego prędkość wyraża się poprzez to przyspieszenie.

Elektron przemieszcza się przez kryształ zawierający jony dodatnie, zderzając się z jonami. Te zderzenia odrzucają go w różnych kierunkach. Gdyby nie było przyłożonego pola elektrycznego, średnia prędkość elektronu podczas zderzeń wynosiłaby zero. Jednakże w obecności pola elektrycznego elektron przyspiesza w kierunku przeciwnym do pola pomiędzy zderzeniami, a zatem średnia prędkość, zwana prędkością dryfu, jest zgodna z kierunkiem pola.

Średni czas między kolizjami definiuje się jako średni czas wolny.

Zależność między gęstością prądu a prędkością dryfu wiąże gęstość prądu z polem elektrycznym. Zależność ta ma postać prawa Ohma, z którego można obliczyć przewodność elektryczną materiału.

Ta teoria przewiduje prawidłową zależność przewodności od temperatury. Wraz ze wzrostem temperatury materiału wzrastają wibracje jonów, podobnie jak elektronów. zderzenia z tymi jonami. W związku z tym średni czas wolny maleje, co oznacza, że przewodność maleje. W eksperymentach obserwuje się przewidywanie, że przewodność elektryczna materiału maleje wraz ze wzrostem temperatury, chociaż dokładną zależność można znaleźć wyłącznie stosując mechanikę kwantową.

Teoria przewodnictwa metalicznego

Przewodzenie wolnych elektronów wewnątrz przewodnika najlepiej opisuje mechanika kwantowa. Jednak klasyczny model sprawia, że przewidywania są bliskie ...

Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

Current and Resistance

Natężenie prądu i rezystancja

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

electron drift in metallic conduction

Electron drift in metallic conduction explains how free electrons move through a conductor. A classical model can describe this motion closely, even though quantum mechanics gives the best overall picture. This model is called the theory of metallic conduction.

In this theory, Newton's second law is used to find the acceleration of an electron when an electric field is applied. The electron's velocity is then found from that acceleration. The electron travels through a crystal of positive ions and collides with them. These collisions send the electron in different directions.

If no electric field is present, the average velocity of the electron is zero over many collisions. When an electric field is applied, the electron accelerates opposite to the field between collisions. As a result, the average velocity, called the drift velocity, points in the direction of the field. The average time between collisions is called the mean free time.

The link between current density and drift velocity gives the relationship between current density and electric field. This relationship has the form of Ohm's law, and it can be used to find the electrical conductivity of the material. The theory also predicts the correct temperature trend for conductivity.

As temperature rises, ion vibrations increase. Electrons then collide more often with the ions. The mean free time decreases, so the conductivity decreases. Experiments show this drop in conductivity with increasing temperature. The exact temperature dependence, however, requires quantum mechanics.

Electron Drift in Metallic Conduction

electrical current

Current Flow in Simple Circuits

Electrical current is the flow of charge in a circuit. A large current means a large amount of charge moves through a wire in a short time. A small current means only a small amount of charge moves through the circuit over a longer time. Examples include the current needed to run a refrigerator and the smaller current used by a handheld calculator. The SI unit for current is the ampere, or amp. It is named for the French physicist André-Marie Ampère (1775–1836). One ampere means one coulomb of...

drift velocity

Electrical Current and Electron Drift

Electrical current in a conductor depends on moving charges and the tiny drift speed of those charges. When a free charge enters a wire, it pushes nearby charges ahead because like charges repel each other. That push spreads through the material very quickly, so the electrical signal moves through the system at nearly the speed of light. This fast signal is not the same as the slow motion of each charge. It is a rapidly spreading change in the electric field, often described as an electrical...

current density

Current Density in Wires and Solutions

Current density describes how much electric current passes through a given cross-sectional area. It helps show not just the size of the current, but also how it is distributed through a conductor. The current density can change from point to point because the local charge flow can vary. If the current flow is uniform, the amount of current is the same at every point along the conductor, even when the conductor’s area changes. Current density is measured in amperes per square meter. Its...

resistivity

Resistivity in Conductors and Insulators

Resistivity describes how much a material opposes electric current. When a voltage is applied to a conductor, an electric field forms. The charges in the conductor feel that force, and a current density develops. In some materials, including metals at a given temperature, the current density is approximately proportional to the electric field. In those cases, current density can be modeled with conductivity, written as sigma. Electrical conductivity is measured in (ohm·m)^−1. It tells how well...

resistance

Factors That Affect Electrical Resistance

Electrical resistance describes how much a conductor opposes the flow of current. It is represented by R. When current passes through a conductor, heat is also produced. Resistance is tied to the material’s resistivity, which is a property of the material used to make an electrical component. Resistance is different from resistivity. Resistivity belongs to the material itself, while resistance belongs to the finished component. To study this relationship, consider a wire with length L,...

ohm's law

Measuring Current, Voltage, and Resistance

Ohm's law describes the relationship between current, voltage, and resistance in many materials. In these cases, the current through a substance is directly proportional to the voltage applied to it. The idea was first shown experimentally by German physicist Georg Simon Ohm, who studied current in a metal wire. A material, component, or device that follows this pattern is called ohmic. An ohmic component has a current that increases in step with voltage. A material or component that does not...

non-ohmic devices

Diode Current and Reverse Bias

A diode is a nonohmic circuit element that makes current and voltage behave differently from Ohm’s law. In most substances, current is proportional to the voltage applied, but a diode does not show a linear current-voltage relationship. A diode is a semiconducting device with two terminals: an anode, which is the positive terminal, and a cathode, which is the negative terminal. It allows current to flow in only one direction. In a simple circuit with a battery, a diode, and a resistor, the...

electrical power

Power Limits in Electrical Circuits

Electrical power in a circuit depends on current and voltage. It is the product of these two values and is measured in watts, or joules per second. That relationship helps explain how much energy a circuit can deliver. A car’s auxiliary power outlet is one real-world example. Some outlets are rated at 20 amps and 12 volts, so they can deliver a maximum of 240 watts. That rating shows the upper limit of power the circuit can provide to devices such as a cell phone charger. Bulb wattage also...

electrical energy

Cutting Electric Bills with Efficient Lighting

Electrical energy is the energy transferred when electrons move from one point to another. The longer an appliance is used, the more electrical energy it consumes. If power stays constant, electrical energy equals the power used by the device times the time it runs. That is why longer use leads to a higher electric bill. Electric bills measure this energy in kilowatt-hours. One kilowatt-hour is equal to 3.6 × 10^6 joules. You can lower electrical energy use by cutting the time an appliance...

continuity equation

Charge Conservation and Current Flow

Charge conservation and current flow are linked through the continuity equation. The current density is the amount of current flowing per unit cross-sectional area. The current through a surface can be written as a surface integral of the current density. The conservation of charge says that the total current leaving a volume equals the rate at which charge inside that volume decreases. The total charge can be written using volume charge density, which is a space function. Because of this, the...

boundary conditions for current density

Current Density at Conductivity Boundaries

Current density at a boundary changes when two conducting materials have different electrical conductivities. The normal component of current density stays continuous across the interface. The tangential component, which runs along the surface, becomes discontinuous across the boundary. Consider two conducting media with conductivities σ1 and σ2 separated by an interface. At point P1 in medium 1, the steady current density makes an angle α1 with the normal. At point P2 in medium 2, the current...

electrical conductivity

Resistance and Ohm's Law in Conductors

Resistance and Ohm's law help explain how electric current moves through a conductor. In a perfect conductor, the electric field inside is zero because free electrons move to cancel it. Any extra charge then stays on the surface. In a practical conductor, an applied electric field can remain in place. That field drives electrons through the material and creates a current. The current density, which is current per unit area, is related to the electric field. More generally, it is related to the...

theory of metallic conduction

Electron drift in metallic conduction explains how free electrons move through a conductor. A classical model can describe this motion closely, even though quantum mechanics gives the best overall picture. This model is called the theory of metallic conduction. In this theory, Newton's second law is used to find the acceleration of an electron when an electric field is applied. The electron's velocity is then found from that acceleration. The electron travels through a crystal of positive ions...

key terms and concepts

Explore electron drift, mean free time, and conductivity in metallic conduction. See how electric fields and temperature affect current in metals.

Electron Drift in Metallic Conduction | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

PS.Phy.4.3

Virginia  Standards of Learning

HIgh School

PS.9

PS.9.b

PH.9

PH.9.e

Florida Department of Education

High School

SC.912.P.10

SC.912.P.10.14

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary ...

Average Velocity

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Instantaneous Velocity - I

The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To ...

Instantaneous Velocity - II

Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object ...

Average Acceleration

The importance of understanding acceleration spans our day-to-day experiences, as well as the vast reaches of outer space and the tiny world of subatomic ...

Instantaneous Acceleration

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Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position ...

average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object ...

Acceleration Vectors

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Direction of Acceleration Vectors

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Linear Momentum

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Force and Momentum

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Analyze and interpret data to explain the motion of an object moving with a constant velocity or that is accelerating.

PS.PSc.4.1

Electrical Current

Electrical current is defined as the rate at which charge flows. When there is a large current present, such as that used to run a refrigerator, a large ...

Drift Velocity

The high speed of electrical signals results from the fact that the force between charges acts rapidly at a distance. Thus, when a free charge is forced ...

Current Density

The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, ...

Resistivity

When a voltage is applied to a conductor, an electrical field is generated, and charges in the conductor feel the force due to the electrical field. The ...

Resistance

When a current moves through any conductor, the conductor causes some level of difficulty for the current to flow. The measure of that difficulty is known ...

Ohm's Law

Many materials exhibit a simple relationship between the values of current, voltage, and resistance, known as Ohm&#8217;s law. The current that flows ...

Non-ohmic Devices

In most substances, the current flow is proportional to the voltage applied to it. A simple relationship between the values of current, voltage, and ...

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

PS.PSc.6.2

Continuity Equation

The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area ...

Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current ...

Electrical Conductivity

In perfect conductors, the electric field inside is always zero due to the abundance of free electrons, which nullify any field by flowing. As a result, ...

The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the ...

Obtain, evaluate, and communicate information to explain how current is affected by changes in composition, length, temperature, and diameter of wire.

Magnetism

Magnets are commonly found in everyday objects, such as toys, hangers, elevators, doorbells, and computer devices. Experimentation on these magnets shows ...

Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on ...

Magnetic Field Lines

The representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. Each of the ...

Magnetic Flux

The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). ...

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

Motion Of A Charged Particle In A Magnetic Field

A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move ...

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 ...

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

Magnetic Force On A Current-Carrying Conductor

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

Magnetic Force On Current-Carrying Wires: Example

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

Force On A Current Loop In A Magnetic Field

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

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Biot-Savart Law

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Biot-Savart Law: Problem-Solving

The magnitude and direction of a magnetic field created by a steady current can be calculated using the Biot-Savart law.
Consider a mobile phone battery ...

Magnetic Field Due to Two Straight Wires

Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the ...

magnetic-force-between-two-parallel-currents

Magnetic Force Between Two Parallel Currents

Two long, straight, and parallel current-carrying conductors exert a force of equal magnitude on one another. The direction of the force depends on the ...

Magnetic Field Of A Current Loop

Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the ...

Divergence and Curl of Magnetic Field

The magnetic field due to a volume current distribution given by the Biot&#8211;Savart Law can be expressed as follows:

To evaluate the divergence of the ...

Ampere's Law

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Ampere's Law: Problem-Solving

Ampere&#x27;s law states that for any closed looped path, the line integral of the magnetic field along the path equals the vacuum permeability times the ...

Solenoids

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

Magnetic Field of a Solenoid

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 ...

Toroids

A toroid is a closely wound donut-shaped coil constructed using a single&#xA0; conducting wire. In general, it is assumed that a toriod consists of ...

Use models to explain magnetism in terms of domains, interactions of poles, and magnetic fields.

PS.PSc.6.4

Induction

An emf is induced when the magnetic field in a coil is changed by pushing a bar magnet into or out of the coil. emfs of opposite signs are produced by ...

Faraday's Law

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Lenz's Law

The direction in which the induced emf drives the current around a wire loop can be found through the negative sign. However, it is usually easier to ...

Motional Emf

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Faraday Disk Dynamo

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Induced Electric Fields

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Induced Electric Fields: Applications

An important distinction exists between the electric field induced by a changing magnetic field and the electrostatic field produced by a fixed charge ...

Obtain, evaluate, and communicate information to explain the application of electromagnets.

PS.PSc.6.5

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

Electron Drift in Metallic Conduction

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