Name: current density in wires and solutions
Uploaded: 2023-04-30T12:38:44.000Z
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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.6.2

Current Density

La densité de courant est la quantité totale de courant circulant par unité de section transversale, mesurée en ampères par mètre carré.
Lorsqu’un petit courant circule dans une aire infinitésimale, une relation entre le courant et la densité de courant peut être établie, où thêta est l’angle entre l’aire et la densité de courant. Par conséquent, le courant total traversant la zone peut être déterminé en l’intégrant sur la zone.
Considérons l’intensité de la densité de courant et rappelons l’équation de la vitesse de dérive. En substituant les termes, une relation entre la densité de courant et la vitesse de dérive peut être établie. Alors que le courant est une grandeur scalaire, la densité de courant est une grandeur vectorielle.
Considérons un courant de 0,5 ampère circulant dans une ampoule de 50 watts. L’ampoule est câblée à l’aide d’un fil de cuivre d’un rayon de 1,25 mm. Déterminez l’amplitude de la densité de courant.
Les valeurs connues sont le courant et la section transversale, tandis que la densité de courant est une quantité inconnue. En substituant les quantités connues dans l’équation, la densité de courant peut être déterminée.

<ol>
	<li>OpenStax. (2019). Physique universitaire Vol. 2. [Version Web], p. 394 à 396. Récupéré 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>

densité de courant

La quantité totale de courant qui circule à travers une unité de valeur d'une section transversale est appelée densité de courant. Si le flux de courant est uniforme, la quantité de courant circulant à travers un conducteur est la même en tout point du conducteur, même si la surface du conducteur varie. La densité de courant est composée de la grandeur locale et de la direction du flux de charge, qui varie d'un point à un autre. La densité de courant est mesurée en ampères par mètre carré et la direction est définie comme le flux net de charges positives à travers la zone. De plus, pour un courant donné, à mesure que le diamètre du fil dans un circuit augmente, la densité de charge diminue. La grandeur de la densité de courant est le courant divisé par la surface.

<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;" />

Ainsi, la densité de courant peut être déterminée comme suit :

<img alt="Equation3" src="/files/ftp_upload/13745/13745_Equation_3v2.svg" style="text-align: center; height: 22px;" />

Si q est positif, la vitesse de dérive est dans la même direction que le champ électrique. Si q est négatif, la vitesse de dérive est dans la direction opposée au champ électrique. De toute façon, la direction de la densité de courant est dans la direction du champ électrique. Par exemple, dans une solution de chlorure de sodium, le courant peut être porté à la fois par des ions sodium positifs et des ions chlore négatifs ; le courant total est obtenu en additionnant les courants dus à chaque type de particule chargée.

Densité de courant

La quantité totale de courant circulant à travers une valeur unitaire d’une section transversale est appelée densité de courant. Si le flux de courant est uniforme, ...

Education

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Physics

Physique

Unit 1

Unité 1

Current and Resistance

Courant et résistance

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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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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

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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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Waves and Their Applications in Technologies for Information Transfer

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Position and Displacement

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Average Velocity

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PS.PSc.4.1

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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

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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

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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

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Magnetic Force On A Current-Carrying Conductor

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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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Consider a point charge moving with a ...

Biot-Savart Law

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magnetic-force-between-two-parallel-currents

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Magnetic Field Of A Current Loop

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Divergence and Curl of Magnetic Field

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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 ...

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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