Name: charge conservation and current flow
Uploaded: 2023-09-18T17:11:18.000Z
Duration: 1 min 20 s
Channel: JoVE

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.6.3

Continuity Equation

الكثافة الحالية هي المقدار الإجمالي للتيار المتدفق لكل وحدة مساحة مقطعية. لذلك ، يمكن التعبير عن إجمالي التيار الذي يمر عبر منطقة المقطع العرضي على أنه تكامل السطح لكثافة التيار.
الآن ، يتطلب حفظ الشحنة أن يكون إجمالي التيار المتدفق من حجم معين مساويا لمعدل انخفاض الشحنة داخل هذا الحجم.
للتعبير عن الشحنة الكلية من حيث كثافة شحنة الحجم ، يتم تعديل المعادلة. نظرا لأن كثافة الشحنة هي دالة فضائية ، باستخدام قاعدة لايبنيز ، يمكن تحريك مشتق الوقت داخل التكامل.
يؤدي تطبيق نظرية الاختلاف على الجانب الأيسر من المعادلة إلى تحويل تكامل السطح المغلق إلى تكامل حجمي. هذه العلاقة تنطبق على أي حجم. نتيجة لذلك ، فإن التكاملات متساوية.
تباعد الكثافة الحالية يساوي المعدل السلبي لتغير كثافة شحنة الحجم. تسمى هذه العبارة الرياضية لحفظ الشحنة المحلية بمعادلة الاستمرارية.
بالنسبة للتيارات الثابتة ، تكون كثافة الشحنة ثابتة بمرور الوقت. إذن، تباعد كثافة التيار يساوي صفرا.

<ol>
	<li>جريفيث ، ديفيد ج. ، مقدمة في الديناميكا الكهربائية، كاليفورنيا: بيرسون. ص. 222</li>
	<li>إيدا ، ناثان ، الكهرومغناطيسية الهندسية ، الطبعة الثالثة ، سبرينغر. ص 355-356.</li>
</ol>

معادلة الاستمرارية

<div style="direction:rtl">يُطلق على إجمالي كمية التيار المتدفق لكل وحدة مساحة مقطعية اسم كثافة التيار. وبالتالي، يمكن كتابة التيار المار عبر مساحة مقطعية على أنه التكامل السطحي لكثافة التيار. <img alt="Equation1" src="/files/ftp_upload/14186/14186_Equation_1.png" style="text-align: center; height: 40px;"> وفقًا لمبدأ حفظ الشحنة، فإن إجمالي التيار المتدفق من حجم معين يساوي معدل انخفاض الشحنة ضمن هذا الحجم. <img alt="Equation2" src="/files/ftp_upload/14186/14186_Equation_2.png" style="text-align: center; height: 40px;"> الآن يمكن كتابة الشحنة الإجمالية بدلالة كثافة الشحنة الحجمية. <img alt="Equation3" src="/files/ftp_upload/14186/14186_Equation_3.png" style="text-align: center; height: 40px;"> كثافة الشحنة هي دالة فضائية. وبالتالي، وبتطبيق قاعدة لايبنتز، يمكن نقل المشتق الزمني داخل التكامل. <img alt="Equation4" src="/files/ftp_upload/14186/14186_Equation_4.png" style="text-align: center; height: 40px;"> عند تطبيق نظرية التباعد على الجانب الأيسر من المعادلة أعلاه، يتم تحويل تكامل السطح المغلق إلى تكامل الحجم. <img alt="Equation5" src="/files/ftp_upload/14186/14186_Equation_5.png" style="text-align: center; height: 40px;"> بما أن هذه العلاقة تنطبق على أي حجم، فإن التكاملات متساوية وتسمى العلاقة الناتجة معادلة الاستمرارية. وينص هذا على أن انحراف كثافة التيار يساوي المعدل السلبي لتغير كثافة الشحنة الحجمية. <img alt="Equation6" src="/files/ftp_upload/14186/14186_Equation_6.png" style="text-align: center; height: 40px;"> في حالة التيارات الثابتة، تكون كثافة الشحنة ثابتة مع مرور الوقت. وبالتالي يكون تباعد كثافة التيار صفراً.</div>

يطلق على الكمية الإجمالية للتيار المتدفق لكل وحدة مساحة مقطع عرضي الكثافة الحالية. ومن ثم ، فإن التيار الذي يمر عبر منطقة المقطع العرضي ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

Current and Resistance

التيار والمقاومة

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

charge conservation and current flow

Charge conservation and current flow are linked through the continuity equation. The current density is the amount of current flowing per unit cross-sectional area. The current through a surface can be written as a surface integral of the current density.

The conservation of charge says that the total current leaving a volume equals the rate at which charge inside that volume decreases. The total charge can be written using volume charge density, which is a space function. Because of this, the time derivative can be moved inside the integral by applying the Leibniz rule.

Next, the divergence theorem is used on the left-hand side. This changes the closed surface integral into a volume integral. Since the relation must hold for any volume, the integrands must be equal. This gives the continuity equation, which states that the divergence of the current density equals the negative rate of change of volume charge density. For steady currents, the charge density does not change with time, so the divergence of the current density is zero.

Charge Conservation and Current Flow

electrical current

Current Flow in Simple Circuits

Electrical current is the flow of charge in a circuit. A large current means a large amount of charge moves through a wire in a short time. A small current means only a small amount of charge moves through the circuit over a longer time. Examples include the current needed to run a refrigerator and the smaller current used by a handheld calculator. The SI unit for current is the ampere, or amp. It is named for the French physicist André-Marie Ampère (1775–1836). One ampere means one coulomb of...

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Electrical Current and Electron Drift

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current density

Current Density in Wires and Solutions

Current density describes how much electric current passes through a given cross-sectional area. It helps show not just the size of the current, but also how it is distributed through a conductor. The current density can change from point to point because the local charge flow can vary. If the current flow is uniform, the amount of current is the same at every point along the conductor, even when the conductor’s area changes. Current density is measured in amperes per square meter. Its...

resistivity

Resistivity in Conductors and Insulators

Resistivity describes how much a material opposes electric current. When a voltage is applied to a conductor, an electric field forms. The charges in the conductor feel that force, and a current density develops. In some materials, including metals at a given temperature, the current density is approximately proportional to the electric field. In those cases, current density can be modeled with conductivity, written as sigma. Electrical conductivity is measured in (ohm·m)^−1. It tells how well...

resistance

Factors That Affect Electrical Resistance

Electrical resistance describes how much a conductor opposes the flow of current. It is represented by R. When current passes through a conductor, heat is also produced. Resistance is tied to the material’s resistivity, which is a property of the material used to make an electrical component. Resistance is different from resistivity. Resistivity belongs to the material itself, while resistance belongs to the finished component. To study this relationship, consider a wire with length L,...

ohm's law

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non-ohmic devices

Diode Current and Reverse Bias

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electrical power

Power Limits in Electrical Circuits

Electrical power in a circuit depends on current and voltage. It is the product of these two values and is measured in watts, or joules per second. That relationship helps explain how much energy a circuit can deliver. A car’s auxiliary power outlet is one real-world example. Some outlets are rated at 20 amps and 12 volts, so they can deliver a maximum of 240 watts. That rating shows the upper limit of power the circuit can provide to devices such as a cell phone charger. Bulb wattage also...

electrical energy

Cutting Electric Bills with Efficient Lighting

Electrical energy is the energy transferred when electrons move from one point to another. The longer an appliance is used, the more electrical energy it consumes. If power stays constant, electrical energy equals the power used by the device times the time it runs. That is why longer use leads to a higher electric bill. Electric bills measure this energy in kilowatt-hours. One kilowatt-hour is equal to 3.6 × 10^6 joules. You can lower electrical energy use by cutting the time an appliance...

continuity equation

Charge conservation and current flow are linked through the continuity equation. The current density is the amount of current flowing per unit cross-sectional area. The current through a surface can be written as a surface integral of the current density. The conservation of charge says that the total current leaving a volume equals the rate at which charge inside that volume decreases. The total charge can be written using volume charge density, which is a space function. Because of this, the...

boundary conditions for current density

Current Density at Conductivity Boundaries

Current density at a boundary changes when two conducting materials have different electrical conductivities. The normal component of current density stays continuous across the interface. The tangential component, which runs along the surface, becomes discontinuous across the boundary. Consider two conducting media with conductivities σ1 and σ2 separated by an interface. At point P1 in medium 1, the steady current density makes an angle α1 with the normal. At point P2 in medium 2, the current...

electrical conductivity

Resistance and Ohm's Law in Conductors

Resistance and Ohm's law help explain how electric current moves through a conductor. In a perfect conductor, the electric field inside is zero because free electrons move to cancel it. Any extra charge then stays on the surface. In a practical conductor, an applied electric field can remain in place. That field drives electrons through the material and creates a current. The current density, which is current per unit area, is related to the electric field. More generally, it is related to the...

theory of metallic conduction

Electron Drift in Metallic Conduction

Electron drift in metallic conduction explains how free electrons move through a conductor. A classical model can describe this motion closely, even though quantum mechanics gives the best overall picture. This model is called the theory of metallic conduction. In this theory, Newton's second law is used to find the acceleration of an electron when an electric field is applied. The electron's velocity is then found from that acceleration. The electron travels through a crystal of positive ions...

key terms and concepts

Learn how charge conservation leads to the continuity equation, how current density relates to charge flow, and why steady currents have zero divergence.

Charge Conservation and Current Flow | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

PS.Phy.4.3

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PS.PSc.6.2

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Charge Conservation and Current Flow

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