What is displacement current?

Short Answer

Displacement current is a term introduced by Maxwell to explain how a changing electric field can behave like an electric current. It is not a real flow of charges but a mathematical quantity that allows magnetic fields to exist even in regions where no actual current flows.
It is given by:
Iₑ = ε₀ (dΦₑ/dt)

Displacement current is important because it completes Ampere’s law and helps in the formation of electromagnetic waves.

Detailed Explanation :

Displacement Current

Displacement current is a key concept in electromagnetism that explains how magnetic fields can arise even when there is no real flow of electric charges. It was introduced by James Clerk Maxwell to solve a major problem in Ampère’s law. Before Maxwell’s correction, Ampère’s law worked only for steady (unchanging) currents. Whenever the electric field changed with time, the law failed to give correct results. To fix this, Maxwell added a new term called displacement current, which allowed Ampère’s law to work universally.

Displacement current plays a central role in linking electricity and magnetism and is essential in explaining how electromagnetic waves travel through space.

Definition of Displacement Current

Displacement current refers to the quantity:

Iₑ = ε₀ (dΦₑ/dt)

where:

  • Iₑ = displacement current
  • ε₀ = permittivity of free space
  • dΦₑ/dt = rate of change of electric flux

It acts like a current because it creates a magnetic field just like a real current does.

Why Maxwell Introduced Displacement Current

Maxwell introduced this idea to solve an important inconsistency in Ampère’s law. Consider a simple circuit with a charging capacitor. The wire carries current, but between the plates of the capacitor, no electrons actually travel because there is an insulating gap.

According to Ampère’s original law, the magnetic field should depend on the current passing through the loop. But if we draw a surface across the gap between the capacitor plates, the current appears to be zero, which would give contradictory results for the magnetic field.

Maxwell solved this by proposing that a changing electric field between the plates acts like a current. This “imaginary” current is the displacement current.

Displacement Current Between Capacitor Plates

When a capacitor charges:

  • Electrons accumulate on one plate and leave the other.
  • The electric field between the plates increases.
  • This changing electric field produces a displacement current.

Although no electrons move across the gap, the displacement current ensures continuity and produces the same magnetic effect as a real current in the wires.

Thus, even in the absence of charge flow, a changing electric field can create magnetic fields.

Difference Between Real Current and Displacement Current

Real (Conduction) Current Displacement Current
Involves movement of charges (electrons). Does not involve movement of charges.
Exists in conductors. Exists in space and insulators.
Produces magnetic fields. Also produces magnetic fields.

Even though they are different, both produce magnetic effects, which is why Maxwell included both in Ampère’s law.

Ampere-Maxwell Law and Displacement Current

The corrected Ampère’s law becomes:

∮B · dl = μ₀ (I + ε₀ dΦₑ/dt)

Here, I is real current, and Iₑ is displacement current. With this addition, the law now works perfectly in all situations—steady or changing.

This correction completed the symmetry between electricity and magnetism.

Role in Electromagnetic Waves

Displacement current is crucial for the existence of electromagnetic waves. Here’s why:

  • A changing electric field produces a magnetic field (through displacement current).
  • A changing magnetic field produces an electric field (Faraday’s law).

These two processes support each other and allow waves to travel through space. Without displacement current, electromagnetic waves could not exist.

Thus, displacement current is the bridge that allows light, radio waves, and all EM waves to propagate.

Physical Meaning

Even though displacement current is not a real current, it represents the effect of the changing electric field. It tells us that magnetic fields can exist anywhere electric fields change, even in vacuum.

Thus, displacement current explains:

  • Magnetic fields between capacitor plates
  • Magnetic fields in regions with no conduction
  • Field behaviour in dielectrics
  • Propagation of electromagnetic waves

Applications of Displacement Current

Displacement current plays an important role in many technologies:

  • Charging and discharging of capacitors
  • Operation of AC circuits
  • Antennas transmitting radio waves
  • Wireless communication systems
  • Capacitor filters in electronics
  • Electromagnetic wave propagation

Without displacement current, many modern electrical and communication systems would not function.

Importance in Physics

Maxwell’s introduction of displacement current is considered one of the most brilliant ideas in physics. It unified Ampère’s law with Faraday’s law, created Maxwell’s equations, and proved that electromagnetic waves are possible. It also contributed to the development of modern field theory and Einstein’s relativity later.

Conclusion

Displacement current is a term introduced by Maxwell to describe how a changing electric field can act like a current and produce a magnetic field. It is essential for explaining the behaviour of capacitors, the symmetry of Maxwell’s equations, and the existence of electromagnetic waves. Although no actual charges move during displacement current, it plays a vital role in the propagation of energy and fields in electromagnetism.