Definition of Displacement Current
Provides the mathematical definition of displacement current, Id = ε₀ (dΦE / dt), relating it to the rate of change of electric flux.
What is Definition of Displacement Current?
A term introduced by Maxwell, proportional to the rate of change of electric flux, which acts as a source of magnetic field just like conduction current.
Key formula / rule: Displacement Current
Key points
- Understand the need for displacement current.
- Define displacement current mathematically.
- Relate displacement current to changing electric flux.
- Recognize the significance of displacement current in electromagnetism.
Common exam trap
Confusing displacement current with conduction current.
Definitions
- Term
Displacement Current
- Meaning
A term introduced by Maxwell, proportional to the rate of change of electric flux, which acts as a source of magnetic field just like conduction current.
- Term
Electric Flux (ΦE)
- Meaning
A measure of the electric field passing through a given surface area.
Learning objectives
Understand the need for displacement current.
Define displacement current mathematically.
Relate displacement current to changing electric flux.
Recognize the significance of displacement current in electromagnetism.
Formulae
- Name
Displacement Current
- Note
Where Id is displacement current, ε₀ is the permittivity of free space, and dΦE/dt is the rate of change of electric flux.
- Expression
Id = ε₀ \frac{d\ΦE}{dt}
- Name
Electric Flux
- Note
Electric flux through a surface is the integral of the electric field over that surface.
- Expression
\ΦE = \int \vec{E} \· d\vec{A}
Prerequisites
Electric Flux
Gauss's Law
Ampere's Law
Capacitors
Common mistakes
Confusing displacement current with conduction current.
Forgetting the proportionality constant ε₀.
Not understanding the role of electric flux change.
Keywords
Displacement Current
Maxwell
Electric Flux
Ampere's Law
Electromagnetic Waves
Capacitor
ε₀
Practice preview
What is the unit of displacement current?…
easy
The electric flux through a closed surface is given by Φ_E = 5t² + 2t + 10 Weber-meter. What is the displacement current at t = 2 seconds?…
medium
The displacement current is proportional to:…
easy