Displacement Current and EM Wave Nature
Maxwell's correction, transverse character and speed of light. (Physics › Electromagnetic Waves, NEET UG syllabus.)
What is Displacement Current and EM Wave Nature?
A current that arises from a changing electric field or electric flux, proposed by Maxwell to maintain the consistency of Ampere's circuital law in situations like a charging capacitor. It produces a magnetic field similar to conduction current.
Key formula / rule: Displacement Current
Key points
- Define displacement current and explain its necessity.
- State the Ampere-Maxwell law.
- Explain how Maxwell's equations predict the existence of electromagnetic waves.
- Describe the nature of electromagnetic waves (transverse, self-propagating).
Common exam trap
Confusing displacement current with conduction current; they are different in origin but have similar magnetic effects.
Definitions
- Term
Displacement Current
- Meaning
A current that arises from a changing electric field or electric flux, proposed by Maxwell to maintain the consistency of Ampere's circuital law in situations like a charging capacitor. It produces a magnetic field similar to conduction current.
- Term
Electromagnetic Waves
- Meaning
Waves that are created as a result of vibrations between an electric field and a magnetic field. They are self-propagating, transverse waves that can travel through a vacuum at the speed of light.
Learning objectives
Define displacement current and explain its necessity.
State the Ampere-Maxwell law.
Explain how Maxwell's equations predict the existence of electromagnetic waves.
Describe the nature of electromagnetic waves (transverse, self-propagating).
Recall the speed of electromagnetic waves in vacuum and its relation to μ₀ and ε₀.
Formulae
- Name
Displacement Current
- Note
Where ε₀ is the permittivity of free space and dΦE/dt is the rate of change of electric flux.
- Expression
Id = ε₀ (dΦE/dt)
- Name
Ampere-Maxwell Law
- Note
Where Ic is the conduction current and Id = ε₀ (dΦE/dt) is the displacement current.
- Expression
∮ B ⋅ dl = μ₀ (Ic + ε₀ (dΦE/dt))
- Name
Speed of Electromagnetic Waves in Vacuum
- Note
Where μ₀ is the permeability of free space and ε₀ is the permittivity of free space.
- Expression
c = 1 / √(μ₀ε₀)
Prerequisites
Basic understanding of electric fields and electric flux.
Basic understanding of magnetic fields and magnetic flux.
Ampere's Circuital Law.
Faraday's Law of Electromagnetic Induction.
Concept of Gauss's Law for electricity and magnetism.
Common mistakes
Confusing displacement current with conduction current; they are different in origin but have similar magnetic effects.
Forgetting the ε₀ factor in the displacement current formula.
Not understanding that EM waves are self-propagating due to mutual generation of E and B fields.
Incorrectly stating the direction of E, B, and propagation (they are mutually perpendicular).
Assuming EM waves need a medium to travel.
Keywords
Displacement current
Maxwell's equations
Electromagnetic waves
Ampere-Maxwell law
Speed of light
Transverse waves
Electric flux
Magnetic field
Permittivity
Permeability
Practice preview
Which of the following expressions correctly represents the displacement current (Id)?…
easy
What is the fundamental nature of electromagnetic waves?…
easy
An electromagnetic wave is propagating along the positive x-axis. If the electric field oscillates along the y-axis, then the magnetic field must oscillate along the:…
medium