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electrical_engineering_and_electronics_1:block11 [2025/11/08 14:26] – mexleadminelectrical_engineering_and_electronics_1:block11 [2026/01/10 13:41] (aktuell) – mexleadmin
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 ===== Block 11 — Influence and Displacement Field ====== ===== Block 11 — Influence and Displacement Field ======
  
-===== Learning objectives =====+===== 11.0 Intro ===== 
 + 
 +==== 11.0.1 Learning Objectives ====
 <callout> <callout>
 After this 90-minute block, you can After this 90-minute block, you can
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-===== Preparation at Home =====+==== 11.0.2 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:
   * 5.4.1   * 5.4.1
-  * +  * 5.4.4 
 +  * 5.4.5
  
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-===== 90-minute plan =====+==== 11.0.3 90-minute plan ====
   - Warm-up (10 min):   - Warm-up (10 min):
     - One-minute recap quiz (Block 10): equipotentials, field lines.     - One-minute recap quiz (Block 10): equipotentials, field lines.
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-===== Conceptual overview =====+==== 11.0.4 Conceptual overview ====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - **Conductors in electrostatics:** free charges move until $E_{\rm inside}=0$; the surface becomes an equipotential and field lines are perpendicular to it. \\ Induced charges live on the surface (surface density $\varrho_A$).   - **Conductors in electrostatics:** free charges move until $E_{\rm inside}=0$; the surface becomes an equipotential and field lines are perpendicular to it. \\ Induced charges live on the surface (surface density $\varrho_A$).
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-===== Core content =====+===== 11.1 Core content =====
  
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-==== Electric Field inside of a conductor ====+==== 11.1.1 Electric Field inside of a conductor ====
  
 As seen in [[https://wiki.mexle.org/electrical_engineering_and_electronics_1/block10#stationary_situation_of_a_charged_conducting_object_without_an_external_field|Block10]], any hole inside a conductor does neither show field lines nor an electric field. This is called  {{wp>Faraday cage}} or Faraday shield. \\ As seen in [[https://wiki.mexle.org/electrical_engineering_and_electronics_1/block10#stationary_situation_of_a_charged_conducting_object_without_an_external_field|Block10]], any hole inside a conductor does neither show field lines nor an electric field. This is called  {{wp>Faraday cage}} or Faraday shield. \\
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-==== Electrostatic Induction ====+==== 11.1.2 Electrostatic Induction ====
  
 In a thought experiment, an uncharged conductor (e.g., a metal plate) is brought into an electrostatic field (<imgref ImgNr11>).  In a thought experiment, an uncharged conductor (e.g., a metal plate) is brought into an electrostatic field (<imgref ImgNr11>). 
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-==== Electric Field inside of an Isolator ====+==== 11.1.3 Electric Field inside of an Isolator ====
  
 But how is it like for an isolator in an external field? \\ But how is it like for an isolator in an external field? \\
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-==== Dielectric Constant (Permittivity) ====+==== 11.1.4 Dielectric Constant (Permittivity) ====
  
 Dielectric materials reduce the electric field inside them. How much die field is reduced is given by a material dependent constant the **dielectric constant** or **permittivity** $\varepsilon_r$. It is unitless and a ratio related to the unhindered field in vacuum. Dielectric materials reduce the electric field inside them. How much die field is reduced is given by a material dependent constant the **dielectric constant** or **permittivity** $\varepsilon_r$. It is unitless and a ratio related to the unhindered field in vacuum.
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-==== Typical Geometries ====+==== 11.1.5 Typical Geometries ====
  
 The "new" $D$-field is a nice tool, which helps to derive the $E$-field more easily. \\ The "new" $D$-field is a nice tool, which helps to derive the $E$-field more easily. \\
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-==== Dielectric strength of dielectrics ====+==== 11.1.6 Dielectric Strength of Dielectrics ====
  
   * The dielectrics act as insulators. The flow of current is therefore prevented   * The dielectrics act as insulators. The flow of current is therefore prevented
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-===== Common pitfalls =====+===== 11.2 Common pitfalls =====
   * Mixing up **cause** and **effect**: using $\oint \vec{E}\cdot{\rm d}\vec{A}$ to count charge. Use **$\vec{D}$** for Gauss’s law with charge; convert to $\vec{E}$ only via $\vec{E}=\vec{D}/(\varepsilon_0\varepsilon_{\rm r})$.   * Mixing up **cause** and **effect**: using $\oint \vec{E}\cdot{\rm d}\vec{A}$ to count charge. Use **$\vec{D}$** for Gauss’s law with charge; convert to $\vec{E}$ only via $\vec{E}=\vec{D}/(\varepsilon_0\varepsilon_{\rm r})$.
   * Forgetting that the **interior of a conductor is field-free** in electrostatics and that $E$ is **normal** to an ideal conducting surface (no tangential $E$ on the surface).   * Forgetting that the **interior of a conductor is field-free** in electrostatics and that $E$ is **normal** to an ideal conducting surface (no tangential $E$ on the surface).
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   * Checking breakdown with voltage only. The limit is on **field** $E$; always relate geometry (e.g., plate spacing, curvature) to $E$ and compare to **$E_0$** with units (e.g., $\,{\rm kV/mm}$).   * Checking breakdown with voltage only. The limit is on **field** $E$; always relate geometry (e.g., plate spacing, curvature) to $E$ and compare to **$E_0$** with units (e.g., $\,{\rm kV/mm}$).
  
-===== Exercises =====+===== 11.3  Exercises =====
 ==== Tasks ==== ==== Tasks ====
  
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-{{page>electrical_engineering_and_electronics_2:task_5.4.2_with_calc&nofooter}} +{{page>electrical_engineering_and_electronics:task_5.4.2_with_calc&nofooter}} 
-{{page>electrical_engineering_and_electronics_2:task_5.4.3&nofooter}} +{{page>electrical_engineering_and_electronics:task_5.4.3&nofooter}} 
-{{page>electrical_engineering_and_electronics_2:task_5.4.4&nofooter}}+{{page>electrical_engineering_and_electronics:task_5.4.4&nofooter}} 
 + 
 +{{page>electrical_engineering_and_electronics:task_ci1z102x25jmpzvs_with_calculation&nofooter}} 
 +{{page>electrical_engineering_and_electronics:task_ic9pioiu0notvwfp_with_calculation&nofooter}} 
 + 
  
 <wrap anchor #exercise_5_4_5 /> <wrap anchor #exercise_5_4_5 />
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-</WRAP></WRAP></panel> 
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- 
-<panel type="info" title="Task 5.5.1 induced Charges"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> 
- 
-A plate capacitor with a distance of $d = 2 ~{ \rm cm}$ between the plates and with air as dielectric ($\varepsilon_{ \rm r}=1$) gets charged up to $U = 5~{ \rm kV}$.  
-In between the plates, a thin metal foil with the area $A = 45~{ \rm cm^2}$ is introduced parallel to the plates.  
- 
-Calculate the amount of the displaced charges in the thin metal foil. 
- 
-<button size="xs" type="link" collapse="Loesung_5_5_1_Tipps">{{icon>eye}} Tips for the solution</button><collapse id="Loesung_5_5_1_Tipps" collapsed="true"> 
-  * What is the strength of the electric field $E$ in the capacitor? 
-  * Calculate the displacement flux density $D$ 
-  * How can the charge $Q$ be derived from $D$? 
-</collapse> 
- 
-<button size="xs" type="link" collapse="Loesung_5_5_1_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_5_5_1_Endergebnis" collapsed="true"> 
-$Q = 10 ~{ \rm nC}$ 
-</collapse> 
  
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 {{youtube>imdtXcnywb8?start=600}} {{youtube>imdtXcnywb8?start=600}}
 </WRAP> </WRAP>
 +
 +<WRAP column half>
 +Parallel-plate capacitor and dielectric breakdown{{youtube>iPes9Ci1CzU?start=61}}
 +</WRAP>
 +
  
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