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Displacement Current - Ampere-Maxwell Law Explained | Testbook.com

Last Updated on Jan 26, 2025

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In the realm of electricity, we often come across two types of currents - the conduction current and the displacement current. While the conduction current arises due to the actual movement of electric charges, the displacement current does not. Let's delve deeper into the concept of displacement current.

Unraveling the Concept of Displacement Current
The displacement current, a term that you will frequently encounter in Maxwell’s equations , is essentially defined by the rate of change of the electric displacement field (D). This concept is best understood by looking at what happens in a capacitor.

The Role of Current in a Capacitor

When a capacitor begins to charge, there is no direct conduction of charge between the plates. However, the changing accumulation of charge over time on the plates alters the electric field, which in turn gives rise to the displacement current. This can be mathematically expressed as:

Here,

S represents the area of the capacitor plate.
I _D signifies the displacement current.
J _D denotes the displacement current density.
D is connected to the electric field E as D = εE
ε is the permittivity of the medium between the plates.

Equation for Displacement Current
The displacement current shares the same unit and has a similar impact on the magnetic field as the conduction current. This is beautifully illustrated in Maxwell’s equation:

In this equation,

H is linked to the magnetic field B as B = μH

μ is the permeability of the medium between the plates.

J stands for the conducting current density.

J _D represents the displacement current density.

Applying the principles of Gauss’s law , we can further simplify the equation to,

Here, ρ is the electric charge density.

What is the SI unit of displacement current?

The SI unit of displacement current is Ampere (A)

How does the displacement current arise?

Displacement current arises due to varying electromotive force.

What is the output of a capacitor connected to displacement current?

Zero

What is displacement current?

The current due to the changing electric field is called displacement current.

Does the displacement current satisfy the property of continuity?

Yes, the sum of displacement and conduction current remains constant along the closed path.

Write the expression for the displacement current.

ID=JDS=S∂D/∂t

What is the magnitude of displacement current in the case of steady electric fields in a conducting wire?

Zero

What current exists inside a capacitor?

The current that exists inside the capacitor is Displacement current.

State Ampere-Maxwell law

The line integral of the magnetic field around a closed loop is equal to μ0 times the sum of conduction current and displacement current.

Why was the concept of displacement current introduced?

Displacement current was introduced to the current in terms of Ampere circuit law to make it logically consistent.

Distinguish between conduction current and displacement current?

Conduction current is due to the flow of electrons in a circuit. It exists even if electrons flow at a uniform rate. Displacement current is due to the time-varying electric field. It does not exist under steady conduction.

What is the magnitude of displacement current in the case of steady electric fields in a conducting wire? Explain.

The magnitude of displacement current in the case of steady electric fields in a conducting wire is zero since the electric field E does not change with time.

How is the concept of displacement current associated with the behaviour of electric and magnetic fields?

According to Faraday’s law of electromagnetic induction, a time-varying magnetic field induces an emf, According to Maxwell, an electric field sets up a current and hence a magnetic field. Such a current is called displacement current. It follows that a time-varying electric field produces a magnetic field and vice-versa. Hence, the behaviour of the electric and magnetic field is symmetric.

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