In classical electromagnetism, displacement current is a term introduced by James Clerk Maxwell to extend Ampère’s Law and make it consistent with the principle of continuity of current in situations where there is no actual flow of free charge, such as in a capacitor or in changing electric fields in empty space.
Displacement current is not a current of moving charges like conduction current in wires, but rather it represents a changing electric field that acts like a current and produces a magnetic field. Mathematically, the displacement current density J<sub>d</sub> is given by:
J<sub>d</sub> = ∂D/∂t
where D is the electric displacement field, which in free space is ε₀E (ε₀ is the permittivity of free space, E is the electric field).
Maxwell modified Ampère’s Law to include the displacement current term:
∇ × B = μ₀(J + ∂D/∂t)
where:
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B is the magnetic field,
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μ₀ is the permeability of free space,
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J is the conduction current density,
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∂D/∂t is the displacement current density.
The significance of the displacement current can be understood in several ways:
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Completion of Maxwell’s Equations:
Before Maxwell, Ampère’s Law only accounted for conduction current. But this created an inconsistency in scenarios like charging a capacitor: between the capacitor plates, there is no conduction current, yet a magnetic field exists in the surrounding region. By introducing the displacement current, Maxwell resolved this contradiction, showing that a changing electric field creates a magnetic field just as moving charges do. -
Prediction of Electromagnetic Waves:
Including displacement current led to the realization that changing electric fields generate changing magnetic fields and vice versa. This interplay forms the basis of electromagnetic wave propagation. Without the displacement current, there would be no theoretical foundation for self-sustaining light waves traveling through empty space. -
Practical Implications:
Displacement current explains why high-frequency currents can pass through capacitors. In AC circuits, capacitors “pass” alternating currents because the changing electric field between their plates creates a displacement current that keeps the circuit continuous even though no physical charge crosses the dielectric. -
Technological Applications:
The concept underlies the functioning of antennas, wireless transmission, waveguides, and modern communication systems. It is fundamental to understanding how radio, microwaves, and light waves travel through space.
In summary, displacement current is essential because it preserves the continuity of current where physical charge does not flow, unifies electric and magnetic fields, and makes possible the propagation of electromagnetic waves — a cornerstone of modern physics and technology.