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

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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.

significance of displacement current

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 conduction current. However, it is produced by a changing electric field. Displacement current is defined in terms of a time-varying electric field, and also has an associated displacement current density. By adding a term accounting for displacement current, Maxwell modified the existing Amp&#xE8;re&#x27;s law, which is now called generalized Amp&#xE8;re&#x27;s law.
<img alt="Equation1" src="/files/ftp_upload/14094/14094_equation_1.svg" style="text-align: center; height: 34px;" />
The presence of displacement current in the region between the plates of a charging capacitor accounts for the continuity of the magnetic field, which can be observed by placing a compass needle in the region between the capacitor plates. The generalized Amp&#xE8;re&#x27;s law can be applied to obtain the magnetic field in the region between the plates of a charging capacitor, where no conduction current is present due to the absence of charge flow.
<img alt="Equation2" src="/files/ftp_upload/14094/14094_equation_2.svg" style="text-align: center; height: 30px;" />
The magnetic field between the plates of the capacitor is found to be zero at the axis and increases linearly with increasing the distance from the axis.

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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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

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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...

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lenz's law

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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...

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.

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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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Maxwell’s Fix for Charging Capacitors

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