Need for Displacement Current
Explains the necessity of introducing an additional current term to resolve the inconsistency of Ampere's law and ensure the principle of charge conservation.
What is Need for Displacement Current?
Current due to the actual flow of charge carriers (e.g., electrons in a wire).
Key formula / rule: Electric Flux
Key points
- Understand the limitation of Ampere's circuital law.
- Explain the concept of displacement current.
- Relate displacement current to changing electric flux.
- State Maxwell's generalized Ampere's law.
Common exam trap
Confusing displacement current with conduction current.
Definitions
- Term
Conduction Current
- Meaning
Current due to the actual flow of charge carriers (e.g., electrons in a wire).
- Term
Displacement Current
- Meaning
A current that is associated with a time-varying electric field or electric flux, introduced by Maxwell.
- Term
Electric Flux
- Meaning
A measure of the electric field passing through a given surface.
Learning objectives
Understand the limitation of Ampere's circuital law.
Explain the concept of displacement current.
Relate displacement current to changing electric flux.
State Maxwell's generalized Ampere's law.
Appreciate the role of displacement current in electromagnetism.
Formulae
- Name
Electric Flux
- Note
Integral of the electric field over a surface.
- Expression
\ΦE = \oint \vec{E} \· d\vec{A}
- Name
Displacement Current
- Note
Proportional to the rate of change of electric flux.
- Expression
Id = \ε0 \frac{d\ΦE}{dt}
- Name
Displacement Current Density
- Note
Current per unit area due to changing electric field.
- Expression
Jd = \ε0 \frac{dE}{dt}
- Name
Maxwell's Generalized Ampere's Law
- Note
Includes both conduction current (Ic) and displacement current (Id).
- Expression
\oint \vec{B} \· d\vec{l} = \μ0 (Ic + Id)
Prerequisites
Electric Flux
Gauss's Law
Capacitance and Capacitors
Ampere's Circuital Law
Conduction Current
Common mistakes
Confusing displacement current with conduction current.
Forgetting that displacement current is generated by a *changing* electric field/flux.
Applying the original Ampere's law in situations with changing electric fields.
Incorrectly calculating electric flux or its rate of change.
Keywords
Displacement Current
Conduction Current
Ampere's Law
Maxwell's Equations
Electric Flux
Charging Capacitor
Electromagnetic Waves
Practice preview
According to Maxwell's theory, a changing electric field is equivalent to which of the following?…
medium
In the context of Maxwell's equations, what is the primary role of displacement current?…
easy
A parallel plate capacitor is being charged. If the rate of change of electric field between the plates is $E'$, then the displacement current density $J_d$ is given by:…
medium