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electrical_engineering_and_electronics_1:block18 [2025/12/02 18:51] – mexleadminelectrical_engineering_and_electronics_1:block18 [2025/12/13 16:12] (aktuell) – mexleadmin
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-====== Block 18 — Magnetic Flux and Inductivity ======+====== Block 18 — Magnetic Flux and Induction ======
  
 ===== Learning objectives ===== ===== Learning objectives =====
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 For checking your understanding please do the following exercises: For checking your understanding please do the following exercises:
-  * ...+  * Exercise E3 Coil in a magnetic Field 
 +  * Exercise 4.1.2 Magnetic Field Strength around a horizontal straight Conductor 
 +  * Exercise 4.1.4 Effects of induction I 
  
 ===== 90-minute plan ===== ===== 90-minute plan =====
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 which is identical to the potential difference between the ends of the rod that we determined earlier. which is identical to the potential difference between the ends of the rod that we determined earlier.
 +
 +<WRAP> <imgcaption ImgNr10 | motional Induction on a single Rod revisited> </imgcaption> {{drawio>MotionalInductionExampleRod2.svg}} </WRAP>
  
 ==== Linked Flux ==== ==== Linked Flux ====
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 ===== Exercises ===== ===== Exercises =====
 +
 +{{page>electrical_engineering_and_electronics:task_rdz03rspbwusy7wk_with_calculation&nofooter}}
 +{{page>electrical_engineering_and_electronics:task_ludzwiuhjxitz85b_with_calculation&nofooter}}
 +
 +
 +<panel type="info" title="Exercise 4.1.4 Effects of induction I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 +
 +A change of magnetic flux is passing a coil with a single winding. The following pictures <imgref ImgNrEx01> show different flux-time-diagrams as examples.
 +
 +  * Create for each $\Phi(t)$-diagram the corresponding $u_{\rm ind}(t)$-diagram!
 +  * Write down each maximum value of $u_{\rm ind}(t)$
 +
 +<WRAP> <imgcaption ImgNrEx01| Flux-Time-Diagrams> </imgcaption> <WRAP> {{drawio>FluxTimeDia1.svg}} \\ </WRAP></WRAP>
 +
 +<button size="xs" type="link" collapse="Solution_4_1_4_1_Solution">{{icon>eye}} Solution for (a)</button><collapse id="Solution_4_1_4_1_Solution" collapsed="true">
 +
 +For partwise linear $u_{\rm ind}$ one can derive: 
 +\begin{align*} 
 +u_{\rm ind} &= -{{{\rm d}\Phi}\over{{\rm d}t}} \\ 
 +            &= -{{\Delta \Phi}\over{\Delta t}} 
 +\end{align*}
 +
 +For diagram (a):
 +
 +  * $t= 0.0 ... 0.6 ~\rm s$: $u_{\rm ind} = -{{0 ~\rm Vs}\over{0.6 ~\rm s}}= 0$
 +  * $t= 0.6 ... 1.5 ~\rm s$: $u_{\rm ind} = -{{-3.75\cdot 10^{-3} ~\rm Vs}\over{0.9 ~\rm s}}= +4.17 ~\rm mV$
 +  * $t= 1.5 ... 2.1 ~\rm s$: $u_{\rm ind} = -{{0 ~\rm Vs}\over{0.6 ~\rm s}}= 0$
 +
 +</collapse>
 +
 +<button size="xs" type="link" collapse="Solution_4_1_4_1_Finalresult">
 +{{icon>eye}} Final result for (a)</button><collapse id="Solution_4_1_4_1_Finalresult" collapsed="true"> 
 +<WRAP> <imgcaption ImgNrEx01| Flux-Time-Diagrams Solution> </imgcaption> <WRAP> {{drawio>FluxTimeDia1Solution.svg}} \\ 
 +</WRAP></WRAP> \\ 
 +</collapse>
 +
 +</WRAP></WRAP></panel>
 +
 +<panel type="info" title="Exercise 4.1.5 Effects of induction II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 +
 +A changing of magnetic flux is passing a coil with a single winding and induces the voltage $u_{\rm ind}(t)$. 
 +The following pictures <imgref ImgNrEx02> show different voltage-time diagrams as examples.
 +
 +  * Create for each $u_{\rm ind}(t)$-diagram the corresponding $\Phi(t)$-diagram!
 +  * Write down each maximum value of $\Phi(t)$
 +
 +Note the given start value $\Phi_0$ for each flux.
 +
 +<WRAP> <imgcaption ImgNrEx02| Voltage-Time-Diagrams> </imgcaption> <WRAP> {{drawio>FluxTimeDia2.svg}} \\ </WRAP></WRAP>
 +
 +#@HiddenBegin_HTML~415_1S,Solution for (a)~@#
 +
 +For partwise linear $u_{\rm ind}$ one can derive: 
 +\begin{align*} 
 +u_{\rm ind}        &= -{{{\rm d}\Phi}\over{{\rm d}t}} \\ 
 +\rightarrow  \Phi  &= -\int_0^t{ u_{\rm ind} \;{\rm d}t} \\
 +\Phi               &= \Phi_0 -\sum_k {u_{{\rm ind},~k} \; \Delta t} \\
 +\end{align*}
 +
 +For diagram (a):
 +
 +  * $t= 0.00 ... 0.04 ~\rm s\quad$: $\quad \Phi = \Phi_0 - {0 \cdot \; \Delta t} \quad\quad\quad\quad\quad\quad\quad= 0 ~\rm Wb$
 +  * $t= 0.04 ... 0.10 ~\rm s\quad$: $\quad \Phi =   0 {~\rm Wb} - {{30 ~\rm mV} \cdot \; (t - 0.04 ~\rm s)} = \quad {1.2 ~\rm mWb} - t \cdot 30 ~\rm mV$
 +  * $t= 0.10 ... 0.14 ~\rm s\quad$: $\quad \Phi =   {1.2 ~\rm mWb} - {0.10 ~\rm s} \cdot 30 ~\rm mV \quad = - {1.8 ~\rm mWb}$
 +
 +#@HiddenEnd_HTML~415_1S,Solution ~@#
 +
 +#@HiddenBegin_HTML~415_1R,Result for (a)~@#
 +{{drawio>FluxTimeDia2Res.svg}} 
 +#@HiddenEnd_HTML~415_1R,Result~@#
 +
 +
 +</WRAP></WRAP></panel>
 +
 +
  
 <panel type="info" title="Exercise 4.1.1 Magnetic Field Strength around a horizontal straight Conductor"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Exercise 4.1.1 Magnetic Field Strength around a horizontal straight Conductor"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
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 </collapse> </WRAP></WRAP></panel> </collapse> </WRAP></WRAP></panel>
  
-{{page>electrical_engineering_and_electronics:task_rdz03rspbwusy7wk_with_calculation&nofooter}} 
-{{page>electrical_engineering_and_electronics:task_ludzwiuhjxitz85b_with_calculation&nofooter}} 
  
- 
-<panel type="info" title="Exercise 4.1.4 Effects of induction I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> 
- 
-A change of magnetic flux is passing a coil with a single winding. The following pictures <imgref ImgNrEx01> show different flux-time-diagrams as examples. 
- 
-  * Create for each $\Phi(t)$-diagram the corresponding $u_{\rm ind}(t)$-diagram! 
-  * Write down each maximum value of $u_{\rm ind}(t)$ 
- 
-<WRAP> <imgcaption ImgNrEx01| Flux-Time-Diagrams> </imgcaption> <WRAP> {{drawio>FluxTimeDia1.svg}} \\ </WRAP></WRAP> 
- 
-<button size="xs" type="link" collapse="Solution_4_1_4_1_Solution">{{icon>eye}} Solution for (a)</button><collapse id="Solution_4_1_4_1_Solution" collapsed="true"> 
- 
-For partwise linear $u_{\rm ind}$ one can derive:  
-\begin{align*}  
-u_{\rm ind} &= -{{{\rm d}\Phi}\over{{\rm d}t}} \\  
-            &= -{{\Delta \Phi}\over{\Delta t}}  
-\end{align*} 
- 
-For diagram (a): 
- 
-  * $t= 0.0 ... 0.6 ~\rm s$: $u_{\rm ind} = -{{0 ~\rm Vs}\over{0.6 ~\rm s}}= 0$ 
-  * $t= 0.6 ... 1.5 ~\rm s$: $u_{\rm ind} = -{{-3.75\cdot 10^{-3} ~\rm Vs}\over{0.9 ~\rm s}}= +4.17 ~\rm mV$ 
-  * $t= 1.5 ... 2.1 ~\rm s$: $u_{\rm ind} = -{{0 ~\rm Vs}\over{0.6 ~\rm s}}= 0$ 
- 
-</collapse> 
- 
-<button size="xs" type="link" collapse="Solution_4_1_4_1_Finalresult"> 
-{{icon>eye}} Final result for (a)</button><collapse id="Solution_4_1_4_1_Finalresult" collapsed="true">  
-<WRAP> <imgcaption ImgNrEx01| Flux-Time-Diagrams Solution> </imgcaption> <WRAP> {{drawio>FluxTimeDia1Solution.svg}} \\  
-</WRAP></WRAP> \\  
-</collapse> 
- 
-</WRAP></WRAP></panel> 
- 
-<panel type="info" title="Exercise 4.1.5 Effects of induction II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> 
- 
-A changing of magnetic flux is passing a coil with a single winding and induces the voltage $u_{\rm ind}(t)$.  
-The following pictures <imgref ImgNrEx02> show different voltage-time diagrams as examples. 
- 
-  * Create for each $u_{\rm ind}(t)$-diagram the corresponding $\Phi(t)$-diagram! 
-  * Write down each maximum value of $\Phi(t)$ 
- 
-Note the given start value $\Phi_0$ for each flux. 
- 
-<WRAP> <imgcaption ImgNrEx02| Voltage-Time-Diagrams> </imgcaption> <WRAP> {{drawio>FluxTimeDia2.svg}} \\ </WRAP></WRAP> 
- 
-#@HiddenBegin_HTML~415_1S,Solution for (a)~@# 
- 
-For partwise linear $u_{\rm ind}$ one can derive:  
-\begin{align*}  
-u_{\rm ind}        &= -{{{\rm d}\Phi}\over{{\rm d}t}} \\  
-\rightarrow  \Phi  &= -\int_0^t{ u_{\rm ind} \;{\rm d}t} \\ 
-\Phi               &= \Phi_0 -\sum_k {u_{{\rm ind},~k} \; \Delta t} \\ 
-\end{align*} 
- 
-For diagram (a): 
- 
-  * $t= 0.00 ... 0.04 ~\rm s\quad$: $\quad \Phi = \Phi_0 - {0 \cdot \; \Delta t} \quad\quad\quad\quad\quad\quad\quad= 0 ~\rm Wb$ 
-  * $t= 0.04 ... 0.10 ~\rm s\quad$: $\quad \Phi =   0 {~\rm Wb} - {{30 ~\rm mV} \cdot \; (t - 0.04 ~\rm s)} = \quad {1.2 ~\rm mWb} - t \cdot 30 ~\rm mV$ 
-  * $t= 0.10 ... 0.14 ~\rm s\quad$: $\quad \Phi =   {1.2 ~\rm mWb} - {0.10 ~\rm s} \cdot 30 ~\rm mV \quad = - {1.8 ~\rm mWb}$ 
- 
-#@HiddenEnd_HTML~415_1S,Solution ~@# 
- 
-#@HiddenBegin_HTML~415_1R,Result for (a)~@# 
-{{drawio>FluxTimeDia2Res.svg}}  
-#@HiddenEnd_HTML~415_1R,Result~@# 
- 
- 
-</WRAP></WRAP></panel> 
  
 <panel type="info" title="Exercise 4.1.6 Coil in magnetic Field I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Exercise 4.1.6 Coil in magnetic Field I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
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 ===== Embedded resources ===== ===== Embedded resources =====
 <WRAP column half> <WRAP column half>
-Explanation (video): ...+How magnetism really works \\ 
 +{{youtube>1TKSfAkWWN0}} 
 +</WRAP> 
 + 
 +<WRAP column half> 
 +Application of Eddy currents \\ 
 +{{youtube>Yu1uRvErM80?start=35}} 
 +</WRAP> 
 + 
 + \\ 
 + 
 +<WRAP column half> 
 +Application of Eddy currents \\ 
 +{{youtube>sENgdSF8ppA}} 
 +</WRAP> 
 + 
 +<WRAP column half> 
 +Magnet in a copper Tube \\ 
 +{{youtube>TRihrPnLt78?start=453}} 
 +</WRAP> 
 + 
 + \\ 
 + 
 +<WRAP column half> 
 +Hall Sensor \\ 
 + 
 +{{url>https://upload.wikimedia.org/wikipedia/commons/transcoded/7/77/Hall_Sensor.webm/Hall_Sensor.webm.480p.vp9.webm}} 
 </WRAP> </WRAP>