Electromagnetism and Charge Conservation

From the study guide

Course Outline

  1. Local Maxwell Equations
  2. Surface and Line Charge
  3. Electric Current Density
  4. Charge Conservation
  5. Stationary Current and Nodes
  6. Integral Gauss and Ampère Laws
  7. Magnetic Flux and Faraday’s Law
  8. Electric Field at a Surface

1. Local Maxwell Equations

★ Must-know

📐 Formula - Maxwell-Gauss’ local equation is div⁡(E⃗)=ρ(M,t)ε0\operatorname{div}(\vec E)=\frac{\rho(M,t)}{\varepsilon_0}.

📐 Formula - Maxwell-Faraday’s local equation is rot⁡(E⃗)=−∂B⃗∂t\operatorname{rot}(\vec E)=-\frac{\partial \vec B}{\partial t}.

📐 Formula - The local magnetic-flux equation is div⁡(B⃗)=0\operatorname{div}(\vec B)=0.

📐 Formula - Maxwell-Ampère’s local equation is rot⁡(B⃗)=μ0j⃗+μ0ε0∂E⃗∂t\operatorname{rot}(\vec B)=\mu_0\vec j+\mu_0\varepsilon_0\frac{\partial \vec E}{\partial t}.

Further detail

  • The vacuum electric permittivity is approximately 8.85×10−12 F⋅m−18.85\times10^{-12}\ \mathrm{F\cdot m^{-1}}.

📐 Formula - The vacuum constants satisfy μ0ε0=1c2\mu_0\varepsilon_0=\frac{1}{c^2}, where cc is the speed of electromagnetic waves in vacuum.

2. Surface and Line Charge

Key Concepts & Definitions

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Practice quiz preview

1. A field measurement gives div⁡(E⃗)=ρ(M,t)ε0\operatorname{div}(\vec E)=\frac{\rho(M,t)}{\varepsilon_0} and a time-varying magnetic field. Which statements correctly identify the local electric-field equations?

2. In a region, the electric field changes with time and a current density is present. Which statements correctly describe the local magnetic-field equations?

3. A surface carries a nonuniform charge density σ(M)\sigma(M). Which statements correctly describe its density and total charge?

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Flashcard preview

What is Maxwell-Gauss’ local equation?

div⁡(E⃗)=ρ(M,t)ε0\operatorname{div}(\vec E)=\frac{\rho(M,t)}{\varepsilon_0}

What is Maxwell-Faraday’s local equation?

rot⁡(E⃗)=−∂B⃗∂t\operatorname{rot}(\vec E)=-\frac{\partial \vec B}{\partial t}

What is the local magnetic-flux equation?

div⁡(B⃗)=0\operatorname{div}(\vec B)=0

What is Maxwell-Ampère’s local equation?

rot⁡(B⃗)=μ0j⃗+μ0ε0∂E⃗∂t\operatorname{rot}(\vec B)=\mu_0\vec j+\mu_0\varepsilon_0\frac{\partial \vec E}{\partial t}

What does surface charge density measure?

Charge per area.

What does linear charge density measure?

Charge per length.

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Frequently asked questions

What does the Electromagnetism and Charge Conservation study guide cover?

It covers the core concepts of Electromagnetism and Charge Conservation, organized by topic with the key definitions, explanations and takeaways, so it's easier to learn and remember.

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How many questions are in the Electromagnetism and Charge Conservation quiz?

The practice quiz has 12 multiple-choice questions, each with an explanation. Use it to check what you know and find your gaps.

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