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electrical_engineering_and_electronics_1:the_magnetostatic_field [2025/09/19 16:40] – mexleadminelectrical_engineering_and_electronics_1:the_magnetostatic_field [2025/09/19 17:23] (aktuell) – mexleadmin
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-====== 3 The magnetostatic Field ======+====== 7 The magnetostatic Field ======
  
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-===== 3.1 Magnetic Phenomena =====+===== 7.1 Magnetic Phenomena =====
  
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-First, permanent magnets made of magnetic magnetite ($\rm Fe_{3} O_{4}$) were found in Greece in the region around Magnesia. Besides the iron materials, other elements also show a similar "strong and permanent magnetic force effect", which is also called ferromagnetism after iron: Cobalt and nickel, as well as many of their alloys, also exhibit such an effect. Chapter [[#3.5 Matter in the magnetic field]] describes the subdivision of magnetic materials in detail.+First, permanent magnets made of magnetic magnetite ($\rm Fe_{3} O_{4}$) were found in Greece in the region around Magnesia. Besides the iron materials, other elements also show a similar "strong and permanent magnetic force effect", which is also called ferromagnetism after iron: Cobalt and nickel, as well as many of their alloys, also exhibit such an effect. Chapter [[#7.5 Matter in the magnetic field]] describes the subdivision of magnetic materials in detail.
  
 Here now the "magnetic force effect" is to be looked at more near. For this purpose, a few thought experiments are carried out with a magnetic iron stone <imgref BildNr01> ([[https://www.youtube.com/watch?v=IgtIdttfGVw|This video]] gives a similar introduction). Here now the "magnetic force effect" is to be looked at more near. For this purpose, a few thought experiments are carried out with a magnetic iron stone <imgref BildNr01> ([[https://www.youtube.com/watch?v=IgtIdttfGVw|This video]] gives a similar introduction).
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 ~~PAGEBREAK~~~~CLEARFIX~~ ~~PAGEBREAK~~~~CLEARFIX~~
  
-===== 3.2 Magnetic Field Strength =====+===== 7.2 Magnetic Field Strength =====
  
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 In the English literature often the name **{{wp>Magnetomotive Force}}** $\mathcal{F}$ is used instead of magnetic voltage $\theta$. The naming refers to the {{wp>Electromotive Force}}. The electromotive force describes the root cause of a (voltage) source to be able to drive a current and therefore generate a defined voltage. Both "forces" shall not be confused with the mechanical force $\vec{F}= m \cdot \vec{a}$. They only describe the driving cause behind the electric or magnetic fields. The German courses in higher semesters use the term //Magnetische Spannung// - therefore, the English equivalent is introduced here.  In the English literature often the name **{{wp>Magnetomotive Force}}** $\mathcal{F}$ is used instead of magnetic voltage $\theta$. The naming refers to the {{wp>Electromotive Force}}. The electromotive force describes the root cause of a (voltage) source to be able to drive a current and therefore generate a defined voltage. Both "forces" shall not be confused with the mechanical force $\vec{F}= m \cdot \vec{a}$. They only describe the driving cause behind the electric or magnetic fields. The German courses in higher semesters use the term //Magnetische Spannung// - therefore, the English equivalent is introduced here. 
  
-In mathematical terms this leads to: +In mathematical terms this leads to a rather ugly monster:  
 +\begin{align*} 
 +\oint_s \vec{H} \cdot {\rm d} \vec{s} &= \sum_n \cdot I_n = \theta  
 +\end{align*} 
   * The path integral of the magnetic field strength along an arbitrary closed path is equal to the currents through the surface enclosed by the path.   * The path integral of the magnetic field strength along an arbitrary closed path is equal to the currents through the surface enclosed by the path.
   * The magnetic voltage $\theta$ can be given as   * The magnetic voltage $\theta$ can be given as
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 ==== Recap: Application of magnetic Field Strength ==== ==== Recap: Application of magnetic Field Strength ====
  
-Ampere's Circuital Law shall be applied to find the magnetic field strength $H$ inside the toroidal coil (<imgref BildNr25>).+The magnetic voltage shall now be applied to find the magnetic field strength $H$ inside the toroidal coil (<imgref BildNr25>) - just to check how we can work with it.
  
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-  * The closed path ${\rm s}$ is on a revolution of a field line in the center of the coil +We see, that the current $I$ is going through the area $A$ $N$-times. \\ 
-  * The surface $A$ is the enclosed surface  +The magnetic voltage is the current through the surface and therefore is given as $N\cdot I$: 
 This leads to:  This leads to: 
- 
-\begin{align*} 
-\oint_s \vec{H} \cdot {\rm d} \vec{s} &= \iint_A \vec{S} {\rm d}\vec{A} = \theta  
-\end{align*} 
- 
-Since $\vec{H} \uparrow \uparrow {\rm d} \vec{s}$ the term $\vec{H} \cdot {\rm d} \vec{s}$ can be substituted by $H {\rm d}s$: 
- 
-\begin{align*} 
-\oint_s H \cdot {\rm d}s              &= \iint_A \vec{S} {\rm d}\vec{A}  
-\end{align*} 
- 
-The magnetic voltage is the current through the surface and is given as $N\cdot I$:  
  
 \begin{align*} \begin{align*}
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-===== 3.3 Magnetic Flux Density and Lorentz Law =====+===== 7.3 Magnetic Flux Density and Lorentz Law =====
    
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-Please have a look at the German contents (text, videos, exercises) on the page of the [[https://obkp.mint-kolleg.kit.edu/#OBKP_EDYNAMIK_LADUNGSBEWEGUNG|KIT-Brückenkurs >> Lorentz-Kraft]]. The last part "Magnetic field within matter" can be skipped.+For further reading you might have a look at the German contents (text, videos, exercises) on the page of the [[https://obkp.mint-kolleg.kit.edu/#OBKP_EDYNAMIK_LADUNGSBEWEGUNG|KIT-Brückenkurs >> Lorentz-Kraft]]. The last part "Magnetic field within matter" can be skipped.
  
-===== 3.4 Matter in the Magnetic Field =====+===== 7.4 Matter in the Magnetic Field (*) ===== 
 + 
 +<button size="xs" type="link" collapse="NotNeededChapter74">{{icon>eye}} not necessary for the course, but you can still find it , when you click here... </button> 
 +<collapse id="NotNeededChapter74" collapsed="true">
  
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 {{https://upload.wikimedia.org/wikipedia/commons/0/06/Moving_magnetic_domains_by_Zureks.gif|}} {{https://upload.wikimedia.org/wikipedia/commons/0/06/Moving_magnetic_domains_by_Zureks.gif|}}
  
 +</collapse>
  
-===== 3.5 Poynting Vector (not part of the curriculum) ===== 
- 
-  * Clear picture of the Poynting vector along an electric circuit: https://de.cleanpng.com/png-jyy1vj/ 
-  * Good explanation of the Energy flow via a current model: http://amasci.com/elect/poynt/poynt.html 
-  * Very detailed view of the energy flow in an electric circuit: http://sharif.edu/~aborji/25733/files/Energy%20transfer%20in%20electrical%20circuits.pdf 
  
 ===== Tasks ===== ===== Tasks =====
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-<panel type="info" title="Task 3.2.1 Magnetic Field Strength around a horizontal straight Conductor"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 7.2.1 Magnetic Field Strength around a horizontal straight Conductor"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 The current $I_0 = 100~\rm A$ flows in a long straight conductor with a round cross-section. The current $I_0 = 100~\rm A$ flows in a long straight conductor with a round cross-section.
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 \end{align*} \end{align*}
  
-#@HiddenEnd_HTML~202,Result~@#+
  
  
 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-<panel type="info" title="Task 3.2.2 Superposition"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 7.2.2 Superposition"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-<panel type="info" title="Task 3.2.3 Magnetic Potential Difference"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 7.2.3 Magnetic Potential Difference"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
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-<panel type="info" title="Task 3.3.1 magnetic Flux Density"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 7.3.1 magnetic Flux Density"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 A $\rm NdFeB$ magnet can show a magnetic flux density up to $1.2 ~\rm T$ near the surface.  A $\rm NdFeB$ magnet can show a magnetic flux density up to $1.2 ~\rm T$ near the surface. 
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 <wrap #task3_3_2 /> <wrap #task3_3_2 />
  
-<panel type="info" title="Task 3.3.2 Electron in Plate Capacitor with magnetic Field"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 7.3.2 Electron in Plate Capacitor with magnetic Field"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 An electron enters a plate capacitor on a trajectory parallel to the plates.  An electron enters a plate capacitor on a trajectory parallel to the plates.