Name: maxwell’s equations at a point
Uploaded: 2025-05-22T09:06:01.000Z
Duration: 1 min 17 s
Channel: JoVE

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North Carolina K-12 Science Standard Course of Study

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Physical Science

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Motion and Stability- Forces and Interactions

PS.PSc.6.5

Differential Form of Maxwell's Equations

맥스웰의 4개 방정식은 전자기학의 기초를 설명합니다.
발산 정리를 가우스의 법칙에 적용하고 총 전하 밀도 측면에서 닫힌 전하를 다시 작성하면 가우스 법칙의 미분 형식이 제공됩니다.
유사하게, 자기장에 대한 가우스의 법칙에 발산 정리를 적용하면 자기에서 가우스의 법칙의 미분 형태가 제공됩니다.
또한 패러데이의 법칙을 재배열하고 스토크의 정리를 적용하면 패러데이의 법칙이 미분 형태로 제공됩니다.
Ampère-Maxwell 방정식을 고려하십시오.이 방정식에서는 밀폐 된 전류가 전류 밀도의 적분으로 표현 될 수 있습니다.
이제 항을 재정렬하고 Stoke의 정리를 적용하면 Ampère-Maxwell 방정식의 미분 형식이 제공됩니다.
한쪽에는 전기장과 자기장이라는 용어가 있고 다른 쪽에는 이러한 자기장이 생성되어 있다는 것을 알 수 있습니다.
Maxwell 방정식의 적분 형식은 전하 또는 전류를 포함하는 영역의 필드에 적용되는 반면, 미분 형식은 전하 및 전류 밀도가 있는 주어진 지점에 적용됩니다.

<ol>
	<li>David J. Griffiths (2013) 전기역학 입문, 제4판: Pearson. 338-339쪽.</li>
	<li>오픈스택스. (2019). 대학 물리학 Vol. 2. [웹 버전]. 섹션 16.1; 700–703쪽. 원본 주소 <a href="https://openstax.org/books/university-physics-volume-2/pages/16-1-maxwells-equations-and-electromagnetic-waves">https://openstax.org/books/university-physics-volume-2/pages/16-1-maxwells-equations-and-electromagnetic-waves</a></li>
</ol>

맥스웰 방정식의 미분 형태

제임스 클럭 맥스웰(James Clerk Maxwell, 1831~1879)은 19세기 물리학에 중요한 공헌을 한 사람 중 한 명입니다. 그는 아마도 전기법칙과 자기법칙에 대한 기존 지식을 자신의 통찰력과 결합하여 맥스웰 방정식으로 표현되는 포괄적이고 포괄적인 전자기 이론을 형성한 것으로 가장 잘 알려져 있을 것입니다. 전기와 자기의 네 가지 기본법칙은 외르스테드, 쿨롱, 가우스, 패러데이 등 물리학자들의 연구를 통해 실험적으로 발견되었습니다. Maxwell은 이러한 초기 결과에서 논리적 불일치를 발견하고 그 원인으로 앰프리 법칙의 불완전성을 식별했습니다. 맥스웰 방정식과 로렌츠 힘의 법칙은 전기와 자기의 모든 법칙을 포괄합니다.

맥스웰 방정식의 적분 형식에는 공간의 특정 영역에 대한 필드 및 소스 수량의 상호 의존성에 대한 모든 정보가 포함되어 있습니다. 그러나 이러한 방정식을 사용하면 필드 벡터 간의 상호 작용과 개별 지점의 소스 밀도와의 관계를 연구할 수 없습니다. 미분 형식의 맥스웰 방정식은 극소 폐쇄 경로, 표면 및 부피에 적분 형식의 맥스웰 방정식을 적용하여 극한이 점으로 축소되도록 유도할 수 있습니다. 미분 방정식은 주어진 지점에서 전기장 및 자기장 벡터의 공간적 변화를 시간적 변화와 연관시킵니다.

게다가 Maxwell 방정식의 미분 형식은 두 필드의 공간적 변화를 주어진 지점의 전하 및 전류 밀도와 연관시킵니다. 전기장과 자기장의 용어를 한 쪽에서 그룹화하고 이러한 필드를 생성하는 소스를 다른 쪽에서 그룹화하면 전하와 전류가 모든 전자기장을 생성한다는 것을 알 수 있습니다. 맥스웰의 방정식은 전하가 전자기장을 생성한다는 것을 보여주고, 힘의 법칙은 장이 전하에 영향을 미친다는 것을 나타냅니다.

제임스 클러크 맥스웰(James Clerk Maxwell, 1831-1879)은 19세기 물리학에 중요한 공헌을 한 사람 중 한 명이다. 그는 아마도 가장 잘 알려진 것으로 알려져 있습니다.

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

Electromagnetic Induction

전자기 유도

KEY TERMS AND CONCEPTS

주요 용어 및 개념

maxwell’s equations at a point

Maxwell’s equations at a point describe how electric and magnetic fields change in space and time. They connect field behavior to charge and current density at a single location. This point-by-point form is useful when studying electromagnetic fields in detail.

James Clerk Maxwell was a major physicist of the nineteenth century. He combined earlier laws of electricity and magnetism into one electromagnetic theory. The basic experimental laws came from scientists such as Oersted, Coulomb, Gauss, and Faraday. Maxwell also found that earlier results contained logical problems, especially because Ampère’s law was incomplete.

Maxwell’s equations and the Lorentz force law together cover the laws of electricity and magnetism. The integral forms of Maxwell’s equations describe the relationship between fields and sources over a region in space. They do not, however, show how field vectors relate to source densities at individual points.

The differential form is found by applying the integral equations to very small closed paths, surfaces, and volumes. As these shapes shrink to points, the equations become local. This form links spatial changes in the electric and magnetic fields to their time changes. It also links those field changes to charge and current densities at the same point.

When the equations are grouped this way, the electric and magnetic fields appear on one side and the sources appear on the other. This arrangement shows that charges and currents produce electromagnetic fields. The force laws then show that fields act back on charges.

Maxwell’s Equations at a Point

induction

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differential form of maxwell's equations

Maxwell’s equations at a point describe how electric and magnetic fields change in space and time. They connect field behavior to charge and current density at a single location. This point-by-point form is useful when studying electromagnetic fields in detail. James Clerk Maxwell was a major physicist of the nineteenth century. He combined earlier laws of electricity and magnetism into one electromagnetic theory. The basic experimental laws came from scientists such as Oersted, Coulomb,...

dc generator

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faraday's law

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lenz's law

Magnet Motion and Induced Current

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motional emf

Induced Current from Changing Magnetic Flux

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faraday disk dynamo

Faraday Disk Dynamo and DC Output

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induced electric fields

Faraday’s Law and Induced EMF

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induced electric fields: applications

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eddy currents

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displacement current

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significance of displacement current

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electromagnetic fields

Electric and Magnetic Fields in Motion

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maxwell's equation of electromagnetism

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key terms and concepts

Learn how Maxwell’s equations in differential form describe electric and magnetic fields at a single point, and how charges and currents create them.

Maxwell’s Equations at a Point | JoVE K12

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PS.Phy.5.2

Virginia  Standards of Learning

HIgh School

PS.9

PS.9.e

Position and Displacement

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Average Velocity

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average-and-instantaneous-velocity-vectors

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PS.PSc.4.1

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Current Density

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Resistivity

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Resistance

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PS.PSc.6.2

Continuity Equation

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Theory of Metallic Conduction

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PS.PSc.6.3

Magnetism

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Magnetic Fields

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Magnetic Field Lines

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Magnetic Flux

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motion-of-a-charged-particle-in-a-magnetic-field

Motion Of A Charged Particle In A Magnetic Field

A charged particle experiences a force when moving through a magnetic field. Consider the field to be uniform and the charged particle to move ...

Magnetic Force

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magnetic-force-on-a-current-carrying-conductor

Magnetic Force On A Current-Carrying Conductor

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magnetic-force-on-current-carrying-wires-example

Magnetic Force On Current-Carrying Wires: Example

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force-on-a-current-loop-in-a-magnetic-field

Force On A Current Loop In A Magnetic Field

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torque-on-a-current-loop-in-a-magnetic-field

Torque On A Current Loop In A Magnetic Field

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magnetic-force-between-two-parallel-currents

Magnetic Force Between Two Parallel Currents

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Magnetic Field Of A Current Loop

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Divergence and Curl of Magnetic Field

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To evaluate the divergence of the ...

Ampere's Law

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Solenoids

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PS.PSc.6.4

Analyze motion in terms of speed, velocity, acceleration, and momentum.

Maxwell’s Equations at a Point

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