by If you are studying Chapter 8: Electromagnetic Waves in your Class 12 Physics textbook, the very first hurdle you face is a strange concept called Displacement Current.
It sounds contradictory. We learned in current electricity that current is the flow of physical charges (electrons). Yet, suddenly, Maxwell tells us there is a “current” flowing through the empty space between capacitor plates where no charges exist.
Why was this concept introduced? Is it a real current? How does it relate to the CBSE Class 12 Syllabus for 2025-26?
Let’s break down this crucial concept that forms the foundation of electromagnetic waves.
The Problem: Ampere’s Circuital Law Was Incomplete
Before James Clerk Maxwell, the laws of electricity and magnetism seemed solid. One fundamental law was Ampere’s Circuital Law, which stated that a magnetic field is generated by an electric current flowing through a wire.
The formula was:
![\[\oint \vec{B} \cdot d\vec{l} = \mu_{0}I_{c}\]](https://i0.wp.com/physicsqanda.com/wp-content/ql-cache/quicklatex.com-ad1130a9df303e5bab68acd39012c558_l3.png?resize=119%2C40&ssl=1 "Rendered by QuickLaTeX.com")
(Where 
is the conduction current flowing through the wire).
Maxwell found a major inconsistency in this law when applied to a capacitor that is being charged.
The Capacitor Paradox
) but failed for the empty gap (
), even though a magnetic field was detected there.Imagine a parallel plate capacitor being charged by a battery.
- Outside the plates: Current flows through the connecting wires. If you place a compass near the wire, it deflects, proving a magnetic field exists. Ampere’s law works here.
- Inside the plates: Between the plates, there is air or vacuum. No physical charge carriers flow across this gap. Therefore, the conduction current (
) is zero. According to old Ampere’s law, the magnetic field between the plates should also be zero.
But here is the catch: Experiments showed that a magnetic field does exist between the plates while the capacitor is charging.
There was a “missing term” in Ampere’s law. Something other than flowing electrons was creating a magnetic field.
The Solution: Maxwell’s Displacement Current
) induces a magnetic field.” class=”wp-image-1643″ style=”aspect-ratio:16/9;object-fit:cover”/>
).Maxwell realized that while physical charge wasn’t crossing the gap between the plates, something else was changing rapidly: The Electric Field (
) and Electric Flux (
).
As the capacitor charges, charge accumulates on the plates, causing the electric field between them to increase with time.
Maxwell proposed a bold idea: A changing electric field (or changing electric flux) acts just like a regular current and produces a magnetic field.
He called this “equivalent current” the Displacement Current.
Defining Displacement Current (For Your Boards)
This is the definition and formula you need to know for your CBSE exams.
Definition:
Displacement current (
Unlike conduction current, it is not caused by the actual movement of electrons.
The Formula for Displacement Current
Through mathematical derivation (which relies on Gauss’s Law), Maxwell defined the displacement current () as:
![\[I_{d} = \varepsilon_{0} \frac{d\Phi_{E}}{dt}\]](https://i0.wp.com/physicsqanda.com/wp-content/ql-cache/quicklatex.com-260fe3d23a3326da613cf092ec0294ba_l3.png?resize=92%2C36&ssl=1 "Rendered by QuickLaTeX.com")
Where:
- = Permittivity of free space
- = Rate of change of electric flux
= Permittivity of free space
= Rate of change of electric fluxThe Corrected Ampere-Maxwell Law
) in the wire is equal to Displacement Current () in the capacitor gap.” class=”wp-image-1645″ style=”aspect-ratio:16/9;object-fit:cover”/>
), satisfying the conservation of charge.Maxwell fixed the inconsistency by adding the displacement current term to Ampere’s original equation. The total current is the sum of conduction current () and displacement current ().
The generalized Ampere-Maxwell Law is:
![\[\oint \vec{B} \cdot d\vec{l} = \mu_{0}(I_{c} + I_{d}) = \mu_{0}(I_{c} + \varepsilon_{0} \frac{d\Phi_{E}}{dt})\]](https://i0.wp.com/physicsqanda.com/wp-content/ql-cache/quicklatex.com-e7b0b707a6f995c7ada2c1862f2f0c59_l3.png?resize=315%2C40&ssl=1 "Rendered by QuickLaTeX.com")
Crucial Note for Exams:
- Inside the connecting wires of a circuit, and only exists.
- Inside the gap of a charging capacitor, and only exists.
- Crucially, the value of in the wires exactly equals the value of in the gap. The circuit is continuous!
and only 
and only Quick Comparison: Conduction vs. Displacement Current
For quick revision, here is how the two types of current differ:
| Feature | Conduction Current () | Displacement Current () |
|---|---|---|
| Source | Caused by the actual flow of charges (electrons/ions). | Caused by a time-varying electric field (changing flux). |
| Medium | Requires a conductor (wire). | Can exist in a vacuum, air, or dielectric. |
| Produces Heat? | Yes (Joule heating,  ). | No, it does not produce heat. |
| Magnetic Field | Produces a magnetic field. | Also produces a magnetic field. |
Why Does This Matter?
Understanding displacement current is not just about fixing an old equation. It led to one of the greatest discoveries in physics history.
If a changing electric field produces a magnetic field (displacement current), and we already know from Faraday’s law that a changing magnetic field produces an electric field, it means these two fields can sustain each other.
This realization led Maxwell to predict the existence of Electromagnetic Waves—self-propagating waves of oscillating electric and magnetic fields that travel at the speed of light.
