Name: current density in wires and solutions
Uploaded: 2023-04-30T12:38:44.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

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Motion and Stability- Forces and Interactions

PS.PSc.6.2

Current Density

Плотность тока — это общая величина протекающего тока на единицу площади поперечного сечения, измеряемая в амперах на квадратный метр.
Когда небольшой ток протекает через бесконечно малую область, можно установить связь между током и плотностью тока, где тета — угол между площадью и плотностью тока. Таким образом, общий ток, проходящий через область, может быть определен путем интегрирования его по площади.
Рассмотрим величину плотности тока и вспомним уравнение скорости дрейфа. Подставляя эти слагаемые, можно установить связь между плотностью тока и скоростью дрейфа. В то время как ток является скалярной величиной, плотность тока является векторной величиной.
Рассмотрим ток в 0,5 ампера, протекающий через 50-ваттную лампочку. Колба подключается с помощью медного провода радиусом 1,25 мм. Определите величину плотности тока.
Известными величинами являются площадь тока и поперечного сечения, в то время как плотность тока является неизвестной величиной. Подставляя известные величины в уравнение, можно определить плотность тока.

<ol>
	<li>OpenStax. (2019). Университетская физика Том 2. [Веб-версия], стр. 394 - 396. Получено из <a href="https://openstax.org/books/university-physics-volume-2/pages/9-2-model-of-conduction-in-metals">https://openstax.org/books/university-physics-volume-2/pages/9-2-model-of-conduction-in-metals</a></li>
</ol>

Плотность тока

Общее количество тока, протекающего через единицу поперечного сечения, называется плотностью тока. Если ток равномерный, то количество тока, протекающего через проводник, одинаково во всех точках проводника, даже если площадь проводника меняется. Плотность тока состоит из локальной величины и направления движения заряда, которые изменяются от точки к точке. Плотность тока измеряется в амперах на квадратный метр, а направление определяется как чистый поток положительных зарядов через площадь. Кроме того, для заданного тока с увеличением диаметра провода в цепи плотность заряда уменьшается. Величина плотности тока равна току, делённому на площадь.

<img alt="Equation1" src="/files/ftp_upload/13745/13745_Equation_1.svg" style="text-align: center; height: 28px;" />

<img alt="Equation2" src="/files/ftp_upload/13745/13745_Equation_2v2.svg" style="text-align: center; height: 14px;" />

Таким образом, плотность тока может быть определена как:

<img alt="Equation3" src="/files/ftp_upload/13745/13745_Equation_3v2.svg" style="text-align: center; height: 22px;" />

Если q положительно, скорость дрейфа направлена в том же направлении, что и электрическое поле. Если q отрицательно, скорость дрейфа направлена в противоположном направлении относительно электрического поля. В любом случае направление плотности тока совпадает с направлением электрического поля. Например, в растворе хлорида натрия ток может быть перенесён как положительными ионами натрия, так и отрицательными ионами хлора; общий ток определяется путём сложения токов, обусловленных каждым видом заряженных частиц.

Общая величина тока, протекающая через одну единицу площади поперечного сечения, называется плотностью тока. Если ток протекает равномерно, ...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Current and Resistance

Ток и сопротивление

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 direction is defined by the net flow of positive charges through the area.

For a given current, a larger wire diameter means a lower charge density. The magnitude of current density is found by dividing current by area. The direction of current density matches the direction of the electric field.

The drift velocity of charged particles depends on charge sign. If q is positive, the drift velocity is in the same direction as the electric field. If q is negative, the drift velocity is opposite to the electric field. In sodium chloride solution, both sodium ions and chlorine ions can carry current, so the total current is the sum of the current from each type of charged particle.

Current Density in Wires and Solutions

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 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...

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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

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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...

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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

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 current density in wires and sodium chloride solution. Learn how current, area, charge sign, and electric field determine its direction and size.

Current Density in Wires and Solutions | JoVE K12

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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.

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Waves and Their Applications in Technologies for Information Transfer

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New York State Science Learning Standards

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HS-PS3-6.

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

To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position ...

Instantaneous Velocity - I

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Instantaneous Velocity - II

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Average Acceleration

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Position and Displacement Vectors

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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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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 ...

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.

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, ...

Theory of Metallic Conduction

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

Magnetism

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Magnetic Field Lines

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

Motion Of A Charged Particle In A Magnetic Field

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Magnetic Force

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Magnetic Force On A Current-Carrying Conductor

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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

Magnetic forces on wires carrying current are most frequently applied in motors. A DC motor is a device that converts electrical energy into mechanical ...

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

Torque On A Current Loop In A Magnetic Field

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The Hall Effect

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Magnetic Field due to Moving Charges

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Consider a point charge moving with a ...

Biot-Savart Law

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Biot-Savart Law: Problem-Solving

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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

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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

A fundamental property of a static magnetic field is that it is not conservative, unlike an electrostatic field. Instead, there is a relationship between ...

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

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

Current Density in Wires and Solutions

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