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electrical_engineering_and_electronics_1:block14 [2025/11/08 14:28] – mexleadminelectrical_engineering_and_electronics_1:block14 [2026/01/10 12:50] (current) – mexleadmin
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 ====== Block 14 - The steady Conduction Field ====== ====== Block 14 - The steady Conduction Field ======
  
-===== Learning objectives =====+===== 14.0 Intro ===== 
 + 
 +==== 14.0.1 Learning objectives ====
 <callout> <callout>
 After this 90-minute block, you can After this 90-minute block, you can
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 </callout> </callout>
  
-===== Preparation at Home =====+==== 14.0.2 Preparation at Home ====
  
 Well, again  Well, again 
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   * 2.2.2   * 2.2.2
  
-===== 90-minute plan =====+==== 14.0.3 90-minute plan ====
   - Warm-up (10 min):   - Warm-up (10 min):
     - Quick recap of Block 11 field pictures (parallel plates, coax) → link to resistance by replacing $\varepsilon$ with $\sigma$.     - Quick recap of Block 11 field pictures (parallel plates, coax) → link to resistance by replacing $\varepsilon$ with $\sigma$.
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     - Summary box (key formulas, units); **Common pitfalls** checklist and Q&A.     - Summary box (key formulas, units); **Common pitfalls** checklist and Q&A.
  
-===== Conceptual overview =====+==== 14.0.4 Conceptual overview ====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - **Analogy:** Replace *displacement flow* in dielectrics ($\vec{D}=\varepsilon\vec{E}$, charge storage) by **flow density** in conductors ($\vec{J}=\sigma\vec{E}$, charge transport). \\ Driving cause is still the electric field $\vec{E}$; the material parameter changes from $\varepsilon$ to $\sigma=\dfrac{1}{\rho}$.   - **Analogy:** Replace *displacement flow* in dielectrics ($\vec{D}=\varepsilon\vec{E}$, charge storage) by **flow density** in conductors ($\vec{J}=\sigma\vec{E}$, charge transport). \\ Driving cause is still the electric field $\vec{E}$; the material parameter changes from $\varepsilon$ to $\sigma=\dfrac{1}{\rho}$.
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 </callout> </callout>
  
-===== Core content =====+===== 14.1 Core content =====
  
 In the discussion of the electrostatic field in principle, no charges in motion were considered. \\ In the discussion of the electrostatic field in principle, no charges in motion were considered. \\
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     * The resistance value is given as: \begin{align*} \boxed{ {{1}\over{R}}=\dfrac{2\pi\sigma l}{\ln(r_a/r_i)} }_\text{between coaxial plates}\end{align*}     * The resistance value is given as: \begin{align*} \boxed{ {{1}\over{R}}=\dfrac{2\pi\sigma l}{\ln(r_a/r_i)} }_\text{between coaxial plates}\end{align*}
  
-===== Common pitfalls =====+===== 14.2 Common pitfalls =====
   * Mixing **$\vec{D}$** (electrostatics) with **$\vec{j}$** (conduction). Use $\vec{D}=\varepsilon\vec{E}$ for capacitors, $\vec{j}=\sigma\vec{E}$ for resistive flow.   * Mixing **$\vec{D}$** (electrostatics) with **$\vec{j}$** (conduction). Use $\vec{D}=\varepsilon\vec{E}$ for capacitors, $\vec{j}=\sigma\vec{E}$ for resistive flow.
   * Forgetting **surface orientation** in $I=\iint_A \vec{j}\cdot{\rm d}\vec{A}$ (normal must align with the chosen current reference arrow).   * Forgetting **surface orientation** in $I=\iint_A \vec{j}\cdot{\rm d}\vec{A}$ (normal must align with the chosen current reference arrow).
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-===== Exercises =====+===== 14.3 Exercises =====
  
 <panel type="info" title="Task 2.2.1 Simulation"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Task 2.2.1 Simulation"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>