Name: maxwell’s equations at a point
Uploaded: 2025-05-22T09:06:01.000Z
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K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

motion-and-stability-forces-and-interactions

Motion and Stability- Forces and Interactions

PS.PSc.6.5

Differential Form of Maxwell's Equations

Maxwell'in dört denklemi elektromanyetizmanın temellerini açıklar.
Diverjans teoremini Gauss yasasına uygulamak ve ekteki yükü toplam yük yoğunluğu cinsinden yeniden yazmak, Gauss yasasının diferansiyel biçimini verir.
Benzer şekilde, manyetik alan için Gauss yasasına ıraksama teoremi uygulamak, manyetizmada Gauss yasasının diferansiyel biçimini verir.
Ayrıca, Faraday yasasını yeniden düzenlemek ve Stoke teoremini ona uygulamak, Faraday yasasını diferansiyel biçimde verir.
Kapalı akımın akım yoğunluğunun integrali cinsinden ifade edilebildiği Ampère-Maxwell denklemini düşünün.
Şimdi, terimleri yeniden düzenlemek ve ona Stoke teoremini uygulamak, Ampère-Maxwell denkleminin diferansiyel formunu verir.
Bir tarafta elektrik ve manyetik alanlar terimlerini, diğer tarafta bu alanları üreten kaynakları gruplandırmak, tüm elektromanyetik alanların yükler ve akımlar tarafından üretildiğini göstermektedir.
Maxwell denkleminin integral formu, yük veya akım içeren bir bölgedeki alanlar için geçerlidir, oysa diferansiyel form, yük ve akım yoğunlukları ile belirli bir noktada geçerlidir.

<ol>
	<li>David J. Griffiths (2013) Elektrodinamiğe Giriş, Dördüncü Baskı: Pearson. s. 338-339.</li>
	<li>Stax'ı açın. (2019). Üniversite Fiziği Cilt 2. [Web sürümü]. Bölüm 16.1; sayfa 700–703. <a href="https://openstax.org/books/university-physics-volume-2/pages/16-1-maxwells-equations-and-electromagnetic-waves" adresinden alındı>https://openstax.org/books/university-physics-volume-2/pages/16-1-maxwells-equations-and-electromagnetic-waves</a></li>
</ol>

maxwell'in diferansiyel denklemleri

James Clerk Maxwell (1831-1879), 19. yüzyılda fizik alanında önemli katkıda bulunanlardan biridir. Maxwell, elektrik ve manyetizma kanunlarıyla kendisine ait önemli görüşlerini birleştirerek, Maxwell'in denklemleri olarak temsil edilen eksiksiz bir elektromanyetik teori oluşturmuştur. Elektrik ve manyetizma kanunlarının dört temel yasası, Oersted, Coulomb, Gauss ve Faraday gibi fizikçilerin çalışmaları sonucunda deneysel olarak keşfedilmiştir. Maxwell, bu önceki sonuçlarda mantıksal tutarsızlıklar keşfetmiş ve Ampere'in yasası eksikliğini tespit etmiştir. Maxwell'in denklemleri ve Lorentz kuvvet yasası, elektrik ve manyetizma kanunlarını kapsar.

Maxwell'in denklemlerinin integral formu, bir alanın ve kaynak miktarlarının birbirine bağımlılığı hakkında bilgileri belirli bir uzay bölgesi boyunca içerir. Bununla birlikte, bu denklemler alan vektörleri ile kaynak yoğunlukları arasındaki etkileşimi ve ilişkilerini bireysel noktalarda çalışmayı mümkün kılmaz. Maxwell'in denklemlerinin diferansiyel formu, integral formdaki Maxwell denklemlerinin sınırsız kapalı yollar, yüzeyler ve hacimlere uygulanarak noktalara daraltıldığı şekilde türetilebilir. Diferansiyel denklemler, belirli bir noktadaki elektrik ve manyetik alan vektörlerinin mekansal varyasyonlarını zamanla olan varyasyonlarıyla ilişkilendirir.

Ayrıca, Maxwell'in denklemlerinin diferansiyel formu aynı noktadaki her iki alanın da mekansal varyasyonlarını yük ve akım yoğunluklarıyla ilişkilendirir. Elektrik ve manyetik alanların terimlerini bir tarafta gruplandırarak bu alanları üreten kaynakları diğer tarafta göstermek, yüklerin ve akımların tüm elektromanyetik alanları ürettiğini gösterir. Maxwell'in denklemleri, yüklerin elektromanyetik alanları ürettiğini ve kuvvet yasalarının da alanların yükleri etkilediğini belirtir.

Maxwell'in Diferansiyel Denklemleri

James Clerk Maxwell (1831-1879), on dokuzuncu yüzyılda fiziğe önemli katkıda bulunanlardan biriydi. Muhtemelen en iyi sahip olduğu bilinir ...

Education

JoVE Core

Physics

Fizik

Unit 1

Ünite 1

Electromagnetic Induction

Elektromanyetik İndüksiyon

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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

Magnetic Flux and Induced Current

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ampere-maxwell's law: problem-solving

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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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magnetic damping

Eddy Currents and Magnetic Braking

Eddy currents can create strong drag on moving objects. This drag is called magnetic damping. A metallic pendulum bob swinging between the poles of a strong magnet feels this force as it enters and leaves the field, so its motion dies out quickly. The effect is much smaller for a slotted metal plate. As the plate enters the magnetic field, a changing flux induces an emf, or electromotive force. The slots limit the size of the current loops, and nearby loops can carry currents in opposite...

superconductor

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Superconductivity is the state in which a material has no electrical resistance and magnetic fields cannot penetrate it. A material that reaches this state is called a superconductor. The key idea in the transcript is the critical temperature, which is the temperature at which the change happens. Heike Kamerlingh Onnes of Leiden University first observed this behavior in mercury in 1911. He cooled a mercury sample in liquid helium to study how resistance changed with temperature. As the...

types of superconductors

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faraday's law

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lenz's law

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Magnet motion and induced current are linked by Lenz’s law. The law says that the induced emf, or electromotive force, drives current around a wire loop in a direction that opposes the change in magnetic flux that caused it. A moving bar magnet can create this effect in a coil. If the magnet moves toward the coil, the magnetic flux increases and an induced current appears. That current produces a magnetic field that pushes against the stronger field from the magnet. The same idea works in...

motional emf

Induced Current from Changing Magnetic Flux

Induced current from changing magnetic flux depends on how a magnetic field interacts with an area. Magnetic flux changes when the field strength changes, when the area it passes through changes, or when the field turns relative to the surface. When any of these factors vary, the magnetic flux also varies. A change in area can happen in two common ways. The flux through a rectangular loop increases as the loop moves into a magnetic field. The magnetic flux through a rotating coil also changes...

faraday disk dynamo

Faraday Disk Dynamo and DC Output

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induced electric fields: applications

Electric Fields from Changing Magnetism

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significance of displacement current

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electromagnetic fields

Electric and Magnetic Fields in Motion

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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

physics

JoVE Temel Fizik, kinematik, dinamik, akışkanlar mekaniği, statik, dalgalar ve akustik dahil olmak üzere temel fizik konularının teorisini ve uygulamasını kısa ve anlaşılması kolay animasyonlu videolarla tanıtıyor. Ek olarak, sektör içindeki bilim insanı videoları, dünya çapındaki günümüz laboratuvarlarında gerçekleştirilen klasik ve orijinal araştırma deneylerinde ilgili kavramların uygulanmasını göstermektedir.

PS.Phy.5.2

Virginia  Standards of Learning

HIgh School

PS.9

PS.9.e

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary ...

Average Velocity

To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position ...

Instantaneous Velocity - I

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Instantaneous Velocity - II

Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity of an object ...

Average Acceleration

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Instantaneous Acceleration

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration ...

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position ...

average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object ...

Acceleration Vectors

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, &#916;v, therefore the ...

Direction of Acceleration Vectors

Acceleration occurs when velocity changes in magnitude (an increase or decrease in speed), direction, or both. Although acceleration is in the direction ...

Linear Momentum

The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum ...

Force and Momentum

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Analyze and interpret data to explain the motion of an object moving with a constant velocity or that is accelerating.

PS.PSc.4.1

Electrical Current

Electrical current is defined as the rate at which charge flows. When there is a large current present, such as that used to run a refrigerator, a large ...

Drift Velocity

The high speed of electrical signals results from the fact that the force between charges acts rapidly at a distance. Thus, when a free charge is forced ...

Current Density

The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, ...

Resistivity

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Resistance

When a current moves through any conductor, the conductor causes some level of difficulty for the current to flow. The measure of that difficulty is known ...

Ohm's Law

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Non-ohmic Devices

In most substances, the current flow is proportional to the voltage applied to it. A simple relationship between the values of current, voltage, and ...

Construct an explanation to compare simple series and parallel circuits in terms of Ohm's Law.

PS.PSc.6.2

Continuity Equation

The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area ...

Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current ...

Electrical Conductivity

In perfect conductors, the electric field inside is always zero due to the abundance of free electrons, which nullify any field by flowing. As a result, ...

Theory of Metallic Conduction

The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the ...

Obtain, evaluate, and communicate information to explain how current is affected by changes in composition, length, temperature, and diameter of wire.

PS.PSc.6.3

Magnetism

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Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on ...

Magnetic Field Lines

The representation of magnetic fields by magnetic field lines is very useful in visualizing the strength and direction of the magnetic field. Each of the ...

Magnetic Flux

The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). ...

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

In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a ...

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

Magnetic Force On A Current-Carrying Conductor

Moving charges experience a force in a magnetic field. Since the magnetic fields produced by moving charges are proportional to the current, a conductor ...

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

Magnetic Force On Current-Carrying Wires: Example

In a magnetic field, moving charges encounter a force. If a wire contains these moving charges, i.e., if the wire is carrying a current, then a force acts ...

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

Force On A Current Loop In A Magnetic Field

Magnetic forces on wires carrying current are most frequently applied in motors. A DC motor is a device that converts electrical energy into mechanical ...

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

Torque On A Current Loop In A Magnetic Field

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The Hall Effect

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Magnetic Field due to Moving Charges

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Consider a point charge moving with a ...

Biot-Savart Law

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Biot-Savart Law: Problem-Solving

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Consider a mobile phone battery ...

Magnetic Field Due to Two Straight Wires

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magnetic-force-between-two-parallel-currents

Magnetic Force Between Two Parallel Currents

Two long, straight, and parallel current-carrying conductors exert a force of equal magnitude on one another. The direction of the force depends on the ...

Magnetic Field Of A Current Loop

Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the ...

Divergence and Curl of Magnetic Field

The magnetic field due to a volume current distribution given by the Biot&#8211;Savart Law can be expressed as follows:

To evaluate the divergence of the ...

Ampere's Law

A fundamental property of a static magnetic field is that it is not conservative, unlike an electrostatic field. Instead, there is a relationship between ...

Ampere's Law: Problem-Solving

Ampere&#x27;s law states that for any closed looped path, the line integral of the magnetic field along the path equals the vacuum permeability times the ...

Solenoids

A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field for a solenoid is the ...

Use models to explain magnetism in terms of domains, interactions of poles, and magnetic fields.

PS.PSc.6.4

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

Maxwell’s Equations at a Point

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