Name: displacement current in an rc circuit
Uploaded: 2023-09-18T17:11:20.000Z
Duration: 1 min 17 s
Channel: JoVE

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North Carolina K-12 Science Standard Course of Study

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Physical Science

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Motion and Stability- Forces and Interactions

PS.PSc.6.5

Ampere-Maxwell's Law: Problem-Solving

Um capacitor de placa paralela no vácuo está na condição de carregamento. O raio de cada placa é de 5 cm. Em um instante, a corrente de condução que flui através dos fios é de 0,4 A. Qual será a corrente de deslocamento entre as placas neste momento?
Além disso, calcule a densidade da corrente de deslocamento e avalie a taxa de mudança no campo elétrico entre as placas. Calcule o campo magnético induzido entre as placas e plote-o a uma distância de 1 a 5 cm do eixo.
A corrente de deslocamento é expressa em termos de fluxo elétrico, que por sua vez, pode ser obtido em termos de carga.
A corrente de deslocamento é igual à corrente de condução que flui através dos fios, que é de 0,4 Amperes.
Além disso, a densidade de corrente de deslocamento pode ser calculada.
À medida que o capacitor carrega, o campo elétrico entre as placas aumenta, o que é avaliado usando a densidade da corrente de deslocamento e a permissividade do espaço livre.
De acordo com a lei de Ampere-Maxwell, o campo magnético é induzido entre as placas do capacitor, que é calculado para diferentes distâncias do eixo e plotado conforme mostrado.

<ol>
	<li>OpenStax. (2019). Física Universitária Vol. 2. [Versão da Web], páginas 94–95. Obtido de <a href="https://openstax.org/books/university-physics-volume-2/pages/16-1-maxwells-equations-and-electromagnetic-waves">https://openstax.org/books/university-physics-volume-2/pages/16-1-maxwells-equations-and-electromagnetic-waves</a></li>
</ol>

lei de ampère-maxwell: resolução de problemas

Um capacitor de placas paralelas com capacitância C, cujas placas possuem área A e distância de separação d, está conectado a um resistor R e a uma bateria de voltagem V. A corrente começa a fluir em t = 0. Qual é a corrente de deslocamento entre as placas do capacitor no tempo t? A partir das propriedades do capacitor, qual é a corrente real correspondente?

Para resolver o problema, podemos usar as equações da análise de um circuito RC e a versão de Maxwell da lei de Ampère.

Para a primeira parte do problema, a voltagem entre as placas no tempo t é dada por:

<img alt="Equation1" src="/files/ftp_upload/14207/14207_Equation_1.svg" style="text-align: center; height: 35px;" />

Suponha que o eixo z aponte da placa positiva para a placa negativa. Nesse caso, o componente z do campo elétrico entre as placas como função do tempo t é dado por:

<img alt="Equation2" src="/files/ftp_upload/14207/14207_Equation_2.svg" style="text-align: center; height: 38px;" />

Portanto, o componente z da corrente de deslocamento Id entre as placas do capacitor pode ser avaliado como:

<img alt="Equation3" src="/files/ftp_upload/14207/14207_Equation_3.svg" style="text-align: center; height: 37px;" />

onde a capacitância <img alt="Equation 4" src="/files/ftp_upload/14207/14207eq04.png" style="margin: auto;" /> está sendo usada.

Além disso, para resolver a segunda parte do problema acima, a corrente no capacitor depois de o circuito estar fechado pode ser obtida pela carga no capacitor, que, por sua vez, pode ser avaliada usando a expressão para VC. Como resultado, descobre-se que a corrente real no capacitor é a mesma que a corrente de deslocamento.

Lei de Ampère-Maxwell: Resolução de problemas

Um capacitor de placa paralela com capacitância C, cujas placas têm área A e distância de separação d, é conectado a um resistor R e a uma bateria de tensão ...

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Physics

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Electromagnetic Induction

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KEY TERMS AND CONCEPTS

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displacement current in an rc circuit

Displacement current in an RC circuit can be found by tracking the charging capacitor. A parallel-plate capacitor with capacitance C, plate area A, and plate separation d is connected to a resistor R and a battery of voltage V. When the current starts to flow at t = 0, the charge and voltage on the capacitor change with time.

The first step is to use the RC-circuit result for the capacitor voltage at time t. With the z-axis pointing from the positive plate to the negative plate, the electric field between the plates has a z-component that follows that same time dependence. The displacement current between the plates is then evaluated from this electric field and the capacitor relation.

The second step is to find the real current into the capacitor after the circuit is closed. This current is obtained from the charge on the capacitor, using the expression for V_C. The result is that the real current into the capacitor is the same as the displacement current.

Displacement Current in an RC Circuit

induction

Magnetic Flux and Induced Current

Magnetic flux and induced current are linked when a magnetic field changes near a coil. Moving a bar magnet into or out of a coil induces an emf, which is an electromotive force. If the motion goes in the opposite direction, the emf has the opposite sign. Reversing the magnet poles also reverses the direction of the induced emf. The same effect appears when the coil moves instead of the magnet. Relative motion is what matters. A faster motion produces a larger emf. If the magnet and coil stay...

ampere-maxwell's law: problem-solving

Displacement current in an RC circuit can be found by tracking the charging capacitor. A parallel-plate capacitor with capacitance C, plate area A, and plate separation d is connected to a resistor R and a battery of voltage V. When the current starts to flow at t = 0, the charge and voltage on the capacitor change with time. The first step is to use the RC-circuit result for the capacitor voltage at time t. With the z-axis pointing from the positive plate to the negative plate, the electric...

differential form of maxwell's equations

Maxwell’s Equations at a Point

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Magnetic Flux and Induced Emf

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lenz's law

Magnet Motion and Induced Current

Magnet motion and induced current are linked by Lenz’s law. The law says that the induced emf, or electromotive force, drives current around a wire loop in a direction that opposes the change in magnetic flux that caused it. A moving bar magnet can create this effect in a coil. If the magnet moves toward the coil, the magnetic flux increases and an induced current appears. That current produces a magnetic field that pushes against the stronger field from the magnet. The same idea works in...

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Induced Current from Changing Magnetic Flux

Induced current from changing magnetic flux depends on how a magnetic field interacts with an area. Magnetic flux changes when the field strength changes, when the area it passes through changes, or when the field turns relative to the surface. When any of these factors vary, the magnetic flux also varies. A change in area can happen in two common ways. The flux through a rectangular loop increases as the loop moves into a magnetic field. The magnetic flux through a rotating coil also changes...

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Faraday Disk Dynamo and DC Output

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Faraday’s Law and Induced EMF

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induced electric fields: applications

Electric Fields from Changing Magnetism

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displacement current

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Maxwell’s correction to Ampère’s law explains how changing electric fields can create magnetic fields. The key idea is the displacement current, Id, which Maxwell added to the real conduction current, I. This extra term helps the law work when current is not steady. The displacement current is defined using the permittivity of free space, ε0, and the electric flux, ΦE. It is not a real flow of charge. Instead, it is an added term in Maxwell’s equations that acts like current in Ampère’s law. <br...

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Maxwell’s Fix for Charging Capacitors

Maxwell’s fix for a charging capacitor is the displacement current in Ampère’s law. A displacement current is not a flow of charge like conduction current. It comes from a changing electric field. That is why it is defined using a time-varying electric field and has its own displacement current density. Maxwell added this term to the original Ampère’s law. The result is called generalized Ampère’s law. The added displacement current term lets the law work in regions where no charges are moving.

electromagnetic fields

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key terms and concepts

See how displacement current is found in a charging parallel-plate capacitor using RC circuit relations and Maxwell’s version of Ampère’s law.

Displacement Current in an RC Circuit | JoVE K12

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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.

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PS.9

PS.9.e

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

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

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration ...

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 ...

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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

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, &#916;v, therefore the ...

Direction of Acceleration Vectors

Acceleration occurs when velocity changes in magnitude (an increase or decrease in speed), direction, or both. Although acceleration is in the direction ...

Linear Momentum

The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum ...

Force and Momentum

Force and momentum are intimately related. Force acting over time can change momentum, and Newton&#39;s second law of motion can be stated in its most ...

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, ...

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.

PS.PSc.6.3

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

Moving charges experience a force in a magnetic field. Since the magnetic fields produced by moving charges are proportional to the current, a conductor ...

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

Magnetic Force On Current-Carrying Wires: Example

In a magnetic field, moving charges encounter a force. If a wire contains these moving charges, i.e., if the wire is carrying a current, then a force acts ...

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

A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a ...

Biot-Savart Law

The Biot-Savart law gives the magnitude and direction of the magnetic field produced by a current. This empirical law was named in honor of two ...

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

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 ...

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.

Displacement Current in an RC Circuit

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