Ampere-Maxwell Law
Relates the magnetic field to both electric current and a changing electric field (displacement current).
What is Ampere-Maxwell Law?
The flow of electric charge through a conductor, typically due to the movement of free electrons.
Key formula / rule: Ampere-Maxwell Law (Integral Form)
Key points
- Understand the relationship between magnetic fields, electric currents, and changing electric fields.
- Define and calculate displacement current.
- Apply the Ampere-Maxwell Law to solve problems involving time-varying fields.
- Appreciate the unification of electricity and magnetism.
Common exam trap
Forgetting to include the displacement current term when there is a changing electric flux.
Definitions
- Term
Conduction Current
- Meaning
The flow of electric charge through a conductor, typically due to the movement of free electrons.
- Term
Displacement Current
- Meaning
A term introduced by Maxwell, representing the effect of a time-varying electric field, which can generate a magnetic field. It is proportional to the rate of change of electric flux.
- Term
Electric Flux
- Meaning
A measure of the total electric field passing through a given area. It is calculated as the surface integral of the electric field over that area.
Learning objectives
Understand the relationship between magnetic fields, electric currents, and changing electric fields.
Define and calculate displacement current.
Apply the Ampere-Maxwell Law to solve problems involving time-varying fields.
Appreciate the unification of electricity and magnetism.
Recognize the role of the Ampere-Maxwell Law in predicting electromagnetic waves.
Formulae
- Name
Ampere-Maxwell Law (Integral Form)
- Note
Relates the line integral of the magnetic field around a closed loop to the enclosed conduction current and the rate of change of electric flux.
- Expression
\oint \vec{B} \· d\vec{l} = \μ0 (Ienc + \ε0 \frac{d\ΦE}{dt})
- Name
Displacement Current
- Note
The current associated with a changing electric flux, which can produce a magnetic field.
- Expression
Id = \ε0 \frac{d\ΦE}{dt}
- Name
Electric Flux
- Note
The measure of the electric field passing through a given surface.
- Expression
\ΦE = \int \vec{E} \· d\vec{A}
Prerequisites
Gauss's Law for Electricity
Gauss's Law for Magnetism
Faraday's Law of Induction
Concept of Electric Flux
Concept of Magnetic Field
Biot-Savart Law
Ampere's Law (original form)
Common mistakes
Forgetting to include the displacement current term when there is a changing electric flux.
Confusing conduction current with displacement current.
Incorrectly calculating the electric flux (ΦE) through the chosen surface.
Applying the law to situations where the magnetic field is not steady or the current distribution is complex without proper integration.
Keywords
Ampere-Maxwell Law
Displacement Current
Electromagnetism
Maxwell's Equations
Electromagnetic Waves
Electric Flux
Magnetic Field
Conduction Current
Practice preview
The Ampere-Maxwell law states that the line integral of the magnetic field B around any closed loop is equal to:…
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Which term did Maxwell add to Ampere's circuital law to complete it?…
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A parallel plate capacitor is being charged by a current I. Which of the following statements is correct regarding the magnetic field between the plates?…
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