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

A densidade de corrente é a quantidade total de corrente que flui por unidade de área da seção transversal, medida em amperes por metro quadrado.
Quando uma pequena corrente flui através de uma área infinitesimal, uma relação entre a corrente e a densidade de corrente pode ser estabelecida, onde é o ângulo entre a área e a densidade de corrente. Portanto, a corrente total que passa pela área pode ser determinada integrando-a sobre a área.
Considere a magnitude da densidade da corrente e lembre-se da equação da velocidade de deriva. Ao substituir os termos, uma relação entre a densidade de corrente e a velocidade de deriva pode ser estabelecida. Enquanto a corrente é uma quantidade escalar, a densidade de corrente é uma quantidade vetorial.
Considere uma corrente de 0,5 amperes fluindo através de uma lâmpada de 50 watts. A lâmpada é conectada por meio de um fio de cobre com raio de 1,25 mm. Determine a magnitude da densidade de corrente.
Os valores conhecidos são a área atual e a área da seção transversal, enquanto a densidade atual é uma quantidade desconhecida. Ao substituir as quantidades conhecidas na equação, a densidade de corrente pode ser determinada.

<ol>
	<li>OpenStax. (2019). Física Universitária Vol. 2. [Versão da Web], pág. 394 - 396. Obtido de <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>

densidade de corrente

A quantidade total de corrente que flui através de uma unidade de valor de área transversal é referida como densidade de corrente. Se o fluxo de corrente for uniforme, a quantidade de corrente que flui através de um condutor é a mesma em todos os pontos ao longo do condutor, mesmo que a área do condutor varie. A densidade de corrente consiste na magnitude local e direção do fluxo de carga, que varia de ponto para ponto. A densidade de corrente é medida em amperes por metro quadrado, e a direção é definida como o fluxo líquido de cargas positivas através da área. Além disso, para qualquer corrente dada, à medida que o diâmetro do fio em um circuito aumenta, a densidade de carga diminui. A magnitude da densidade de corrente é a corrente dividida pela área.

<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;" />

Assim, a densidade de corrente pode ser determinada como:

<img alt="Equation3" src="/files/ftp_upload/13745/13745_Equation_3v2.svg" style="text-align: center; height: 22px;" />

Se q for positivo, a velocidade de deriva é na mesma direção que o campo elétrico. Se q for negativo, a velocidade de deriva é na direção oposta ao campo elétrico. De qualquer forma, a direção da densidade de corrente é na direção do campo elétrico. Por exemplo, em uma solução de cloreto de sódio, a corrente pode ser transportada tanto pelos íons de sódio positivos quanto pelos íons de cloro negativos; a corrente total é encontrada somando as correntes de cada tipo de partícula carregada.

Densidade de corrente

A quantidade total de corrente que flui através de um valor unitário de uma área de seção transversal é chamada de densidade de corrente. Se o fluxo de corrente for uniforme, ...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Current and Resistance

Corrente e Resistência

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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...

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

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

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

PS.PSc.6.3

PS.Phy.4.3

Tennessee Academic Standards

High School

Energy

PHYS.PS3.11

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HIgh School

PS.9

PS.9.b

PS.9.c

PH.8

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Alabama Course of Study Science

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Waves and Their Applications in Technologies for Information Transfer

9-12.PS.2.3.c

9-12.PS.2.3.d

9-12.P.2.6.b

9-12.P.2.6.d

Florida Department of Education

SC.912.P.10

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PHYS.6.D

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New York State Science Learning Standards

HS. Energy

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

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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

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

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

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Magnetic Fields

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Magnetic Field Lines

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Magnetic Flux

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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 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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Magnetic Field Due to Two Straight Wires

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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

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

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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 ...

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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