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electrical_engineering_and_electronics_1:block14 [2025/11/02 21:32] – mexleadminelectrical_engineering_and_electronics_1:block14 [2026/01/10 12:50] (aktuell) – 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 ====
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 After this 90-minute block, you can After this 90-minute block, you can
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-===== Preparation at Home =====+==== 14.0.2 Preparation at Home ====
  
 Well, again  Well, again 
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 For checking your understanding please do the following exercises: For checking your understanding please do the following exercises:
-  * ...+  * 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 ====
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-  - **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 $\sigma=\dfrac{1}{\rho}$. 
-  - **Global relations:** Voltage is a line integral $U=\int \vec{E}\cdot{\rm d}\vec{s}$; current is a flux integral $I=\iint_A \vec{J}\cdot{\rm d}\vec{A}$. Their ratio defines $G=\dfrac{I}{U}$ and $R=\dfrac{U}{I}$ for a given geometry and material. +  - **Global relations:** Voltage is a line integral $U=\int \vec{E}\cdot{\rm d}\vec{s}$; current is a flux integral $I=\iint_A \vec{J}\cdot{\rm d}\vec{A}$. \\ Their ratio defines $G=\dfrac{I}{U}$ and $R=\dfrac{U}{I}$ for a given geometry and material. 
-  - **Geometry matters:** Uniform fields (parallel plates) give $E=\text{const}$ and simple $G=\dfrac{\sigma A}{l}$. Curved fields (coax) spread with radius → logarithmic dependence.+  - **Geometry matters:** Uniform fields (parallel plates) give $E=\text{const}$ and simple $G=\dfrac{\sigma A}{l}$. \\ Curved fields (coax) spread with radius → logarithmic dependence.
   - **Checks:** Units ($\sigma$ in $\rm S/m$, $G$ in $\rm S$, $R$ in $\Omega$). Limits: \\ $A\!\to\!\infty \Rightarrow R\!\to\!0$ \\ $l\!\to\!0 \Rightarrow R\!\to\!0$ \\ $r_a\!\downarrow r_i \Rightarrow R\!\to\!0$.   - **Checks:** Units ($\sigma$ in $\rm S/m$, $G$ in $\rm S$, $R$ in $\Omega$). Limits: \\ $A\!\to\!\infty \Rightarrow R\!\to\!0$ \\ $l\!\to\!0 \Rightarrow R\!\to\!0$ \\ $r_a\!\downarrow r_i \Rightarrow R\!\to\!0$.
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-===== 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 =====
  
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