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electrical_engineering_and_electronics_1:block10 [2025/11/02 17:18] – mexleadminelectrical_engineering_and_electronics_1:block10 [2026/01/10 12:58] (current) – mexleadmin
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 ====== Block 10 - Field Patterns of key Geometries ====== ====== Block 10 - Field Patterns of key Geometries ======
  
-~~PAGEBREAK~~ ~~CLEARFIX~~ +===== 10.0 Intro ===== 
-===== Learning objectives =====+ 
 +==== 10.0.1 Learning objectives ====
 <callout> <callout>
 By the end of this section, you will be able to: By the end of this section, you will be able to:
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-===== Preparation at Home =====+==== 10.0.2 Preparation at Home ====
  
 And again:  And again: 
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-===== 90-minute plan =====+==== 10.0.3 90-minute plan ====
   * **Warm-up (8–10 min)**     * **Warm-up (8–10 min)**  
     Quick sketches: single charge, dipole, parallel plates. Poll for rules of field lines and equipotentials.     Quick sketches: single charge, dipole, parallel plates. Poll for rules of field lines and equipotentials.
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     Summary map linking **field lines ↔ equipotentials ↔ potential difference** as bridge to capacitors and energy (next blocks).     Summary map linking **field lines ↔ equipotentials ↔ potential difference** as bridge to capacitors and energy (next blocks).
  
-===== Conceptual overview =====+==== 10.0.4 Conceptual overview ====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - **Field lines** visualize $\vec{E}$: start at $+$, end at $-$, never intersect; higher line density ⇔ larger $|\vec{E}|$; lines are **not** particle trajectories.   - **Field lines** visualize $\vec{E}$: start at $+$, end at $-$, never intersect; higher line density ⇔ larger $|\vec{E}|$; lines are **not** particle trajectories.
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== Core content =====+===== 10.1 Core content =====
  
-==== Geometric Distribution of Charges ====+==== 10.1.1 Geometric Distribution of Charges ====
  
 In previous chapters, only single charges (e.g., $Q_1$, $Q_2$) were considered.   In previous chapters, only single charges (e.g., $Q_1$, $Q_2$) were considered.  
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   * Finally, a **space charge** is the term for charges that span a volume. \\ Here, examples are plasmas or charges in extended objects (e.g., the doped volumes in a semiconductor). As with the other charge distributions, a (space) charge density $\rho_V$ can be calculated here: <WRAP centeralign>$\rho_V = {{Q}\over{V}}$</WRAP> or for different charge density in partial volumes: <WRAP centeralign>$\rho_V = {{\Delta Q}\over{\Delta V}} \rightarrow \rho_V(V) ={{\rm d}\over{{\rm d}V}} Q(V)={{\rm d}\over{{\rm d}x}}{{\rm d}\over{{\rm d}y}}{{\rm d}\over{{\rm d}z}} Q(V)$</WRAP>   * Finally, a **space charge** is the term for charges that span a volume. \\ Here, examples are plasmas or charges in extended objects (e.g., the doped volumes in a semiconductor). As with the other charge distributions, a (space) charge density $\rho_V$ can be calculated here: <WRAP centeralign>$\rho_V = {{Q}\over{V}}$</WRAP> or for different charge density in partial volumes: <WRAP centeralign>$\rho_V = {{\Delta Q}\over{\Delta V}} \rightarrow \rho_V(V) ={{\rm d}\over{{\rm d}V}} Q(V)={{\rm d}\over{{\rm d}x}}{{\rm d}\over{{\rm d}y}}{{\rm d}\over{{\rm d}z}} Q(V)$</WRAP>
  
-==== Electric Field Lines ====+==== 10.1.2 Electric Field Lines ====
  
 Electric field lines result from the (fictitious) path of a sample charge. Thus, also electric field lines of several charges can be determined.  Electric field lines result from the (fictitious) path of a sample charge. Thus, also electric field lines of several charges can be determined. 
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Types of Fields depending on the Charge Distribution ====+==== 10.1.3 Types of Fields depending on the Charge Distribution ====
  
 There are two different types of fields: There are two different types of fields:
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 </WRAP> </WRAP>  </WRAP> </WRAP> 
  
-==== Stationary Situation of a charged conducting Object (without an external Field) ====+==== 10.1.4 Stationary Situation of a charged conducting Object (without an external Field) ====
  
 In the first thought experiment, a conductor (e.g., a metal plate) is charged, see <imgref ImgNr10>.  In the first thought experiment, a conductor (e.g., a metal plate) is charged, see <imgref ImgNr10>. 
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Dielectric strength ====+==== 10.1.5 Dielectric strength ====
  
 In [[block03#conductivity_of_matter|Block03]] we had a short look on conductivity of matter. \\ In [[block03#conductivity_of_matter|Block03]] we had a short look on conductivity of matter. \\
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-===== Common pitfalls =====+===== 10.2 Common pitfalls =====
   * Treating field lines as **charge paths**: they are drawings of direction/magnitude of $\vec{E}$, **not** particle trajectories.   * Treating field lines as **charge paths**: they are drawings of direction/magnitude of $\vec{E}$, **not** particle trajectories.
   * Forgetting the **reference charge sign**: line arrows indicate the force on a **positive** test charge; forces on electrons point opposite to the arrows.   * Forgetting the **reference charge sign**: line arrows indicate the force on a **positive** test charge; forces on electrons point opposite to the arrows.
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-===== Exercises =====+===== 10.3 Exercises =====
 <panel type="info" title="Task 1.1.2 Field lines"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Task 1.1.2 Field lines"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
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 </WRAP></WRAP></WRAP></panel> </WRAP></WRAP></WRAP></panel>
  
-{{page>task_1.2.5_with_calc&nofooter}} +{{page>electrical_engineering_and_electronics:task_1.2.5_with_calc&nofooter}} 
-{{page>task_1.2.6&nofooter}} +{{page>electrical_engineering_and_electronics:task_1.2.6&nofooter}} 
-{{page>task_1.2.7&nofooter}} +{{page>electrical_engineering_and_electronics:task_1.2.7&nofooter}}
  
 ===== Embedded resources ===== ===== Embedded resources =====