Name: maxwell’s fix for charging capacitors
Uploaded: 2026-07-09T14:56:36.471Z
Duration: 1 min 28 s
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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.6.5

Significance of Displacement Current

Displacement current is defined in terms of a time-varying electric field and has an associated displacement current density.
To understand the significance, consider a circular-shaped parallel capacitor.
A conduction current flows throughout the wires, but there is no conduction current in the region between the capacitor plates as there is no charge flow.
If a compass needle is placed between the capacitor plates, deflection is observed, confirming the presence of a magnetic field.
Displacement current accounts for this continuity of magnetic field in the region between the capacitor plates.
Applying generalized Ampere&#x27;s law to find the magnetic field between the plates.&#xA0;
For this, consider an Amperian loop with a radius less than that of the capacitor.
The line integral of the magnetic field along this loop equals the magnetic field times the circumference.
The current enclosed by the loop equals the product of current density and the enclosed area.
Thus, the magnetic field between the plates of the capacitor is obtained, which is zero at the axis and increases linearly with increasing distance from the axis.

<ol>
	<li>OpenStax. (2019). Fisica universitaria Vol. 2. [Versione web]. 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>

il significato della corrente di spostamento

Una corrente di spostamento &#xE8; analoga a una corrente reale nella legge di Amp&#xE8;re, partecipando alla legge di Amp&#xE8;re allo stesso modo della consueta corrente di conduzione. Tuttavia, essa &#xE8; prodotta da un campo elettrico variabile nel tempo. La corrente di spostamento &#xE8; definita in termini di un campo elettrico variabile nel tempo e ha anche associata una densit&#xE0; di corrente di spostamento. Aggiungendo un termine che tiene conto della corrente di spostamento, Maxwell ha modificato la legge di Amp&#xE8;re esistente, che ora &#xE8; chiamata legge di Amp&#xE8;re generalizzata.

<img alt="Equation1" src="/files/ftp_upload/14094/14094_equation_1.svg" style="text-align: center; height: 34px;" />

La presenza della corrente di spostamento nella regione tra le piastre di un condensatore in fase di carica tiene conto della continuit&#xE0; del campo magnetico, che pu&#xF2; essere osservata posizionando un ago di una bussola nella regione tra le piastre del condensatore. La legge di Amp&#xE8;re generalizzata pu&#xF2; essere applicata per ottenere il campo magnetico nella regione tra le piastre di un condensatore in fase di carica, dove non &#xE8; presente alcuna corrente di conduzione a causa dell&#x27;assenza di flusso di carica.

<img alt="Equation2" src="/files/ftp_upload/14094/14094_equation_2.svg" style="text-align: center; height: 30px;" />

Il campo magnetico tra le piastre del condensatore si trova essere nullo sull&#x27;asse e aumenta linearmente con l&#x27;aumento della distanza dall&#x27;asse.

Il significato della corrente di spostamento

A displacement current is analogous to a real current in Amp&#xE8;re&#x27;s law, participating in Amp&#xE8;re&#x27;s law the same way as the usual ...

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KEY TERMS AND CONCEPTS

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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. This makes the magnetic field continuous between the plates of a capacitor as it charges.

You can see this idea with a compass needle placed between the capacitor plates. Even though there is no conduction current in the gap, the magnetic field is still present there. Generalized Ampère’s law can be used to find that field. It is zero at the axis and increases linearly as the distance from the axis increases.

Maxwell’s Fix for Charging Capacitors

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

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

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faraday's law

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lenz's law

Magnet Motion and Induced Current

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faraday disk dynamo

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displacement current

Maxwell’s Fix for Changing Currents

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...

significance of displacement current

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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electric generator: alternator

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back emf

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key terms and concepts

Learn how displacement current lets Maxwell’s generalized Ampère’s law explain the magnetic field between charging capacitor plates, even without charge flow.

Maxwell’s Fix for Charging Capacitors | JoVE K12

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PS.Phy.5.2

Virginia  Standards of Learning

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PS.9

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HS. Forces and Interactions

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Position and Displacement

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Position and Displacement Vectors

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Resistivity

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Resistance

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PS.PSc.6.2

Continuity Equation

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Electrical Conductivity

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Theory of Metallic Conduction

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PS.PSc.6.3

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

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PS.PSc.6.4

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

Maxwell’s Fix for Charging Capacitors

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