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electrical_engineering_and_electronics_1:the_electrostatic_field [2025/09/19 12:32] – ↷ Links angepasst, weil Seiten im Wiki verschoben wurden mexleadminelectrical_engineering_and_electronics_1:the_electrostatic_field [2025/09/19 16:04] (aktuell) – [Bearbeiten - Panel] mexleadmin
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-====== 1 The Electrostatic Field ======+====== 5 The Electrostatic Field ======
  
 <callout> <callout>
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 </WRAP> </WRAP>
  
-We had already considered the charge as the central quantity of electricity in the first chapter of the previous semester and recognized it as a multiple of the elementary charge. There was already a mutual force action ([[electrical_engineering_1:preparation_properties_proportions#coulomb-force|the Coulomb-force]]) derived. This will be more fully explained.+We had already considered the charge as the central quantity of electricity in the first chapter and recognized it as a multiple of the elementary charge. There was already a mutual force action ([[electrical_engineering_1:preparation_properties_proportions#coulomb-force|the Coulomb-force]]) derived. This will be more fully explained.
  
 First, we shall define certain terms: First, we shall define certain terms:
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== 1.1 Electric Field and Field Lines =====+===== 5.1 Electric Field and Field Lines =====
  
 <callout> <callout>
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 ==== The Electric Field ==== ==== The Electric Field ====
  
-To determine the electric field, a measurement of its magnitude and direction is now required. The Coulomb force between two charges $Q_1$ and $Q_2$ is known from the first chapter of the previous semester:+To determine the electric field, a measurement of its magnitude and direction is now required. The Coulomb force between two charges $Q_1$ and $Q_2$ is known from the first chapter as:
  
 \begin{align*} \begin{align*}
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 ==== Tasks ==== ==== Tasks ====
-<panel type="info" title="Task 1.1.1 simple task with charges"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.1.1 simple task with charges"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 {{youtube>F0IrBhisJA4}} {{youtube>F0IrBhisJA4}}
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-<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 5.1.2 Field lines"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 Sketch the field line plot for the charge configurations given in <imgref ImgNr04>. \\ Sketch the field line plot for the charge configurations given in <imgref ImgNr04>. \\
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-===== 1.2 Electric Charge and Coulomb Force (reloaded) =====+===== 5.2 Electric Charge and Coulomb Force (reloaded) =====
  
 <callout> <callout>
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 </callout> </callout>
  
-The electric charge and Coulomb force have already been described last semester. However, some points are to be caught up here.+The electric charge and Coulomb force have already been described in the first chapter. However, some points are to be caught up here.
  
 ==== Direction of the Coulomb force and Superposition ==== ==== Direction of the Coulomb force and Superposition ====
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 ==== Tasks ==== ==== Tasks ====
  
-{{page>electrical_engineering_and_electronics_2:task_1.2.1_with_calc&nofooter}} +{{page>electrical_engineering_and_electronics_2:task_5.2.1_with_calc&nofooter}} 
-{{page>electrical_engineering_and_electronics_2:task_1.2.2&nofooter}} +{{page>electrical_engineering_and_electronics_2:task_5.2.2&nofooter}} 
-{{page>electrical_engineering_and_electronics_2:task_1.2.3&nofooter}}+{{page>electrical_engineering_and_electronics_2:task_5.2.3&nofooter}}
  
-<panel type="info" title="Task 1.2.4 Superposition of Charges in 1D"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.2.4 Superposition of Charges in 1D"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 {{youtube>QWOwK-zyEnE}} {{youtube>QWOwK-zyEnE}}
 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-{{page>electrical_engineering_and_electronics_2:task_1.1.3_with_calc&nofooter}} +{{page>electrical_engineering_and_electronics_2:task_5.2.5_with_calc&nofooter}} 
-{{page>electrical_engineering_and_electronics_2:task_1.1.4&nofooter}} +{{page>electrical_engineering_and_electronics_2:task_5.2.6&nofooter}} 
-{{page>electrical_engineering_and_electronics_2:task_1.1.5&nofooter}}+{{page>electrical_engineering_and_electronics_2:task_5.2.7&nofooter}}
  
  
-=====1.3 Work and Potential =====+=====5.3 Work and Potential =====
  
 <callout> <callout>
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 \end{align*} \end{align*}
  
-This concept has already been applied as Kirchhoff's voltage law (mesh theorem) in circuits (see [[electrical_engineering_1/simple_circuits#kirchhoff_s_voltage_law|prevoius semester]]). However, it is also valid in other structures and arbitrary electrostatic fields.+This concept has already been applied as Kirchhoff's voltage law (mesh theorem) in circuits. However, it is also valid in other structures and arbitrary electrostatic fields.
  
 <callout icon="fa fa-exclamation" color="red" title="Note:"> <callout icon="fa fa-exclamation" color="red" title="Note:">
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 </callout> </callout>
  
-=====1.4 Conductors in the Electrostatic Field =====+=====5.4 Conductors in the Electrostatic Field =====
  
 <callout> <callout>
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 Application of electrostatic induction: Protective bag against electrostatic charge/discharge (cf. [[https://www.youtube.com/watch?v=imdtXcnywb8&t=600s|Video]]) Application of electrostatic induction: Protective bag against electrostatic charge/discharge (cf. [[https://www.youtube.com/watch?v=imdtXcnywb8&t=600s|Video]])
  
-<panel type="info" title="Task 1.4.1 Simulation"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.4.1 Simulation"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 <WRAP> <WRAP>
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-{{page>electrical_engineering_and_electronics_2:task_1.4.2_with_calc&nofooter}} +{{page>electrical_engineering_and_electronics_2:task_5.4.2_with_calc&nofooter}} 
-{{page>electrical_engineering_and_electronics_2:task_1.4.3&nofooter}} +{{page>electrical_engineering_and_electronics_2:task_5.4.3&nofooter}} 
-{{page>electrical_engineering_and_electronics_2:task_1.4.4&nofooter}}+{{page>electrical_engineering_and_electronics_2:task_5.4.4&nofooter}}
  
-<wrap anchor #exercise_1_4_5 /> +<wrap anchor #exercise_5_4_5 /> 
-<panel type="info" title="Task 1.4.5 Simulation"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.4.5 Simulation"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 Given is the two-dimensional component shown in <imgref ImgNr148>. The component shall be charged positively. \\ Given is the two-dimensional component shown in <imgref ImgNr148>. The component shall be charged positively. \\
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-=====1.5 The Electric Displacement Field and Gauss's Law of electrostatics =====+=====5.5 The Electric Displacement Field and Gauss's Law of electrostatics =====
  
 <callout> <callout>
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 ==== tasks==== ==== tasks====
  
-<panel type="info" title="Task 1.5.1 induced Charges"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<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 $U = 5~{ \rm kV}$.  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 $U = 5~{ \rm kV}$. 
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 Calculate the amount of the displaced charges in the thin metal foil. Calculate the amount of the displaced charges in the thin metal foil.
  
-<button size="xs" type="link" collapse="Loesung_1_5_1_Tipps">{{icon>eye}} Tips for the solution</button><collapse id="Loesung_1_5_1_Tipps" collapsed="true">+<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?   * What is the strength of the electric field $E$ in the capacitor?
   * Calculate the displacement flux density $D$   * Calculate the displacement flux density $D$
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 </collapse> </collapse>
  
-<button size="xs" type="link" collapse="Loesung_1_5_1_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_1_5_1_Endergebnis" collapsed="true">+<button size="xs" type="link" collapse="Loesung_5_5_1_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_5_5_1_Endergebnis" collapsed="true">
 $Q = 10 ~{ \rm nC}$ $Q = 10 ~{ \rm nC}$
 </collapse> </collapse>
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-<panel type="info" title="Task 1.5.2 Manipulating a Capacitor I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.5.2 Manipulating a Capacitor I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 An ideal plate capacitor with a distance of $d_0 = 7 ~{ \rm mm}$ between the plates gets charged up to $U_0 = 190~{ \rm V}$ by an external source.  An ideal plate capacitor with a distance of $d_0 = 7 ~{ \rm mm}$ between the plates gets charged up to $U_0 = 190~{ \rm V}$ by an external source. 
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   - How does the situation change (electric field/voltage), when the source is not disconnected?   - How does the situation change (electric field/voltage), when the source is not disconnected?
  
-<button size="xs" type="link" collapse="Loesung_1_5_2_Tipps">{{icon>eye}} Tips for the solution</button><collapse id="Loesung_1_5_2_Tipps" collapsed="true">+<button size="xs" type="link" collapse="Loesung_5_5_2_Tipps">{{icon>eye}} Tips for the solution</button><collapse id="Loesung_5_5_2_Tipps" collapsed="true">
   * Consider the displacement flux through a surface around a plate   * Consider the displacement flux through a surface around a plate
 </collapse> </collapse>
  
-<button size="xs" type="link" collapse="Loesung_1_5_2_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_1_5_2_Endergebnis" collapsed="true">+<button size="xs" type="link" collapse="Loesung_5_5_2_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_5_5_2_Endergebnis" collapsed="true">
   - $U_1 = 1.9~{ \rm kV}$, $E_1 = 27~{ \rm kV/m}$    - $U_1 = 1.9~{ \rm kV}$, $E_1 = 27~{ \rm kV/m}$ 
   - $U_1 = 190~{ \rm V}$, $E_1 = 2.7~{ \rm kV/m}$    - $U_1 = 190~{ \rm V}$, $E_1 = 2.7~{ \rm kV/m}$ 
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-<panel type="info" title="Task 1.5.3 Manipulating a Capacitor II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.5.3 Manipulating a Capacitor II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 An ideal plate capacitor with a distance of $d_0 = 6 ~{ \rm mm}$ between the plates and with air as dielectric ($\varepsilon_0=1$) is charged to a voltage of $U_0 = 5~{ \rm kV}$.  An ideal plate capacitor with a distance of $d_0 = 6 ~{ \rm mm}$ between the plates and with air as dielectric ($\varepsilon_0=1$) is charged to a voltage of $U_0 = 5~{ \rm kV}$. 
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-<panel type="info" title="Task 1.5.4 Spherical capacitor"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.5.4 Spherical capacitor"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 Two concentric spherical conducting plates set up a spherical capacitor.  Two concentric spherical conducting plates set up a spherical capacitor. 
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-<panel type="info" title="Task 1.5.5 Applying Gauss's law: Electric Field of a line charge"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.5.5 Applying Gauss's law: Electric Field of a line charge"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 {{youtube>NyRjHj2uy6k}} {{youtube>NyRjHj2uy6k}}
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-=====1.6 Non-Conductors in electrostatic Field =====+=====5.6 Non-Conductors in electrostatic Field =====
  
 <callout> <callout>
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 ==== tasks==== ==== tasks====
  
-<panel type="info" title="Task 1.6.1 Thought Experiment"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.6.1 Thought Experiment"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 Consider what would have happened if the plates had not been detached from the voltage source in the above thought experiment (<imgref ImgNr13>). Consider what would have happened if the plates had not been detached from the voltage source in the above thought experiment (<imgref ImgNr13>).
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-=====1.7 Capacitors =====+=====5.7 Capacitors =====
  
 <callout> <callout>
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-=====1.8 Circuits with Capacitors =====+=====5.8 Circuits with Capacitors =====
  
 <callout> <callout>
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 In the simulation below, besides the parallel connected capacitors $C_1$, $C_2$,$C_3$, an ideal voltage source $U_q$, a resistor $R$, a switch $S$, and a lamp are installed. In the simulation below, besides the parallel connected capacitors $C_1$, $C_2$,$C_3$, an ideal voltage source $U_q$, a resistor $R$, a switch $S$, and a lamp are installed.
   * The switch $S$ allows the voltage source to charge the capacitors.   * The switch $S$ allows the voltage source to charge the capacitors.
-  * The resistor $R$ is necessary because the simulation cannot represent instantaneous charging. The resistor limits the charging current to a maximum value. \\ This leads to the DC circuit transients, explained in the  [[electrical_engineering_1:dc_circuit_transients#time_course_of_the_charging_and_discharging_process|last semester]].+  * The resistor $R$ is necessary because the simulation cannot represent instantaneous charging. The resistor limits the charging current to a maximum value. 
   * The capacitors can be discharged again via the lamp.   * The capacitors can be discharged again via the lamp.
  
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 ====Tasks==== ====Tasks====
  
-<panel type="info" title="Task 1.8.1 Calculating a circuit of different capacitors"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.8.1 Calculating a circuit of different capacitors"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 See https://www.youtube.com/watch?v=vSeSHAmpd4Y See https://www.youtube.com/watch?v=vSeSHAmpd4Y
 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-=====1.9 Configurations of multiple Dielectrics =====+===== 5.9 Configurations of multiple Dielectrics (*) =====
  
 <callout> <callout>
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 \begin{align*} \begin{align*}
 U = \int \limits_{\rm path \, inside \\ the \, capacitor} \! \! \vec{E} \cdot {\rm d} \vec{s} = E_1 \cdot d_1 + E_2 \cdot d_2 + E_3 \cdot d_3 U = \int \limits_{\rm path \, inside \\ the \, capacitor} \! \! \vec{E} \cdot {\rm d} \vec{s} = E_1 \cdot d_1 + E_2 \cdot d_2 + E_3 \cdot d_3
-\tag{1.9.1}+\tag{5.9.1}
 \end{align*} \end{align*}
  
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 \begin{align*} \begin{align*}
 \boxed{     \varepsilon_{ \rm r1}  \cdot E_1  =  \varepsilon_{ \rm r2}  \cdot E_2 = \varepsilon_{ \rm r3}  \cdot E_3           } \boxed{     \varepsilon_{ \rm r1}  \cdot E_1  =  \varepsilon_{ \rm r2}  \cdot E_2 = \varepsilon_{ \rm r3}  \cdot E_3           }
-\tag{1.9.2}+\tag{5.9.2}
 \end{align*} \end{align*}
  
-Using $(1.9.1)$ and $(1.9.2)$ we can also derive the following relationship:+Using $(5.9.1)$ and $(5.9.2)$ we can also derive the following relationship:
 \begin{align*} \begin{align*}
 E_2 = & {{\varepsilon_{ \rm r1}}\over{\varepsilon_{ \rm r2}}}\cdot E_1 , \quad E_3 = {{\varepsilon_{ \rm r1}}\over{\varepsilon_{ \rm r3}}}\cdot E_1 \\  E_2 = & {{\varepsilon_{ \rm r1}}\over{\varepsilon_{ \rm r2}}}\cdot E_1 , \quad E_3 = {{\varepsilon_{ \rm r1}}\over{\varepsilon_{ \rm r3}}}\cdot E_1 \\ 
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 \end{align*} \end{align*}
  
-The formula obtained represents the law of refraction of the field line at interfaces. There is also a hint that for electromagnetic waves (like visible light) the refractive index might depend on the dielectric constant. This is the case. However, in the calculation presented here, electrostatic fields were assumed. In the case of electromagnetic waves, the distribution of energy between the two fields must be taken into account. This is not considered in detail in this course but is explained shortly in task 1.9.1.+The formula obtained represents the law of refraction of the field line at interfaces. There is also a hint that for electromagnetic waves (like visible light) the refractive index might depend on the dielectric constant. This is the case. However, in the calculation presented here, electrostatic fields were assumed. In the case of electromagnetic waves, the distribution of energy between the two fields must be taken into account. This is not considered in detail in this course but is explained shortly in task 5.9.1.
  
  
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 ====Tasks==== ====Tasks====
  
-<panel type="info" title="Task 1.9.1 Layered Capacitor Task"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 5.9.1 Layered Capacitor Task"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 {{youtube>ATXnPRXXDi4}} {{youtube>ATXnPRXXDi4}}
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-<panel type="info" title="Exercise 1.9.2 Further capacitor charging/discharging practice Exercise "> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Exercise 5.9.2 Further capacitor charging/discharging practice Exercise "> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 {{youtube>a-gPuw6JsxQ}} {{youtube>a-gPuw6JsxQ}}
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-<panel type="info" title="Exercise 1.9.3 Further practice charging the capacitor"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Exercise 5.9.3 Further practice charging the capacitor"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 {{youtube>L0S_Aw8pBto}} {{youtube>L0S_Aw8pBto}}
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-<panel type="info" title="Exercise 1.9.4 Charge balance of two capacitors"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Exercise 5.9.4 Charge balance of two capacitors"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 {{youtube>EMdpkDoMXXE}} {{youtube>EMdpkDoMXXE}}
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-<panel type="info" title="Exercise 1.9.5 Capacitor with glass plate"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Exercise 5.9.5 Capacitor with glass plate"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 <WRAP> <WRAP>
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-{{page>electrical_engineering_and_electronics_2:task_1.9.3_with_calculation&nofooter}}+{{page>electrical_engineering_and_electronics_2:task_5.9.3_with_calculation&nofooter}}
  
  
-=====1.10 Summary =====+=====5.10 Summary =====
  
 <WRAP> <WRAP>