Name: displacement current in an rc circuit
Uploaded: 2023-09-18T17:11:20.000Z
Duration: 1 min 17 s
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PS.PSc.6.5

Ampere-Maxwell's Law: Problem-Solving

Un condensatore a piastre parallele nel vuoto è in condizione di carica. Il raggio di ogni piatto è di 5 cm. In un istante, la corrente di conduzione che scorre attraverso i fili è di 0,4 A. Quale sarà la corrente di spostamento tra le piastre in questo momento?
Inoltre, calcola la densità di corrente di spostamento e valuta la velocità di variazione del campo elettrico tra le piastre. Calcolare il campo magnetico indotto tra le piastre e tracciarlo per una distanza di 1-5 cm dall'asse.
La corrente di spostamento è espressa in termini di flusso elettrico, che a sua volta può essere ottenuto in termini di carica.
La corrente di spostamento è uguale alla corrente di conduzione che scorre attraverso i fili, che è di 0,4 Ampere.
Inoltre, è possibile calcolare la densità di corrente di spostamento.
Man mano che il condensatore si carica, il campo elettrico tra le piastre aumenta, che viene valutato utilizzando la densità di corrente di spostamento e la permittività dello spazio libero.
Secondo la legge di Ampere-Maxwell, il campo magnetico viene indotto tra le piastre del condensatore, che viene calcolato per diverse distanze dall'asse e tracciato come mostrato.

<ol>
	<li>OpenStax. (2019). Fisica universitaria Vol. 2. [Versione web], pagine 94-95. Estratto da <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>

legge di ampère-maxwell: risolvere i problemi

Un condensatore a piastre parallele con capacità C, le cui piastre hanno area A e distanza di separazione d, è collegato a un resistore R e a una batteria di tensione V. La corrente inizia a fluire al tempo t = 0. Qual è la corrente di spostamento tra le piastre del condensatore al tempo t? Dalle proprietà del condensatore, qual è la corrispondente corrente reale?

Per risolvere il problema, possiamo utilizzare le equazioni dall'analisi di un circuito RC e la versione di Maxwell della legge di Ampère.

Per la prima parte del problema, la tensione tra le piastre al tempo t è data da:

<img alt="Equation1" src="/files/ftp_upload/14207/14207_Equation_1.svg" style="text-align: center; height: 35px;" />

Supponiamo che l'asse z punti dalla lastra positiva a quella negativa. In questo caso, la componente z del campo elettrico tra le piastre come funzione del tempo t è data da:

<img alt="Equation2" src="/files/ftp_upload/14207/14207_Equation_2.svg" style="text-align: center; height: 38px;" />

Perciò, la componente z della corrente di spostamento Id tra le piastre del condensatore può essere valutata come:

<img alt="Equation3" src="/files/ftp_upload/14207/14207_Equation_3.svg" style="text-align: center; height: 37px;" />

dove viene usata la capacità <img alt="Equation 4" src="/files/ftp_upload/14207/14207eq04.png" style="margin: auto;" />.

Inoltre, per risolvere la seconda parte del problema sopra indicato, la corrente nel condensatore dopo la chiusura del circuito può essere ottenuta dalla carica sul condensatore, che a sua volta può essere valutata utilizzando l'espressione per VC. Di conseguenza, si trova che la corrente reale nel condensatore è la stessa della corrente di spostamento.

Legge di Ampère-Maxwell: risolvere i problemi

Un condensatore a piastre parallele con capacità C, le cui piastre hanno area A e distanza di separazione d, è collegato a un resistore R e a una batteria di tensione ...

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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

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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...

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lenz's law

Magnet Motion and Induced Current

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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

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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

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electromagnetic fields

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Electric and magnetic fields can come from different sources, but they can act in surprisingly similar ways. Static charges create electrostatic fields. These fields are conservative, which means a test charge does no net work after moving around a complete loop. Fields made by changing magnetic fields behave differently. They are not conservative, and they do net work on a charge. That work is proportional to how fast the magnetic flux changes. These fields also do not follow Gauss’s law for...

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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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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 ...

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Instantaneous Velocity - II

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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 ...

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

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Electrical Current

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Resistance

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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.

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Continuity Equation

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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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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

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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). ...

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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

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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 ...

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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 ...

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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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The Hall Effect

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Consider a point charge moving with a ...

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Consider a mobile phone battery ...

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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

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To evaluate the divergence of the ...

Ampere's Law

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Ampere's Law: Problem-Solving

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Solenoids

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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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