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electrical_engineering_and_electronics_1:block16 [2025/11/23 12:18] – mexleadminelectrical_engineering_and_electronics_1:block16 [2026/01/10 12:46] (current) – mexleadmin
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 ====== Block 16 - Ampère's Law and Magnetomotive Force (MMF) ====== ====== Block 16 - Ampère's Law and Magnetomotive Force (MMF) ======
  
-===== Learning objectives =====+===== 16.0 Intro ===== 
 + 
 +==== 16.0.1 Learning objectives ====
 <callout> <callout>
 After this 90-minute block, you can After this 90-minute block, you can
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 </callout> </callout>
  
-===== Preparation at Home =====+==== 16.0.2 Preparation at Home ====
  
 Well, again  Well, again 
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   * ...   * ...
  
-===== 90-minute plan =====+==== 16.0.3 90-minute plan ====
   - Warm-up (x min):    - Warm-up (x min): 
     - ....      - .... 
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   - Wrap-up (x min): Summary box; common pitfalls checklist.   - Wrap-up (x min): Summary box; common pitfalls checklist.
  
-===== Conceptual overview =====+==== 16.0.4  Conceptual overview ====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - ...   - ...
 </callout> </callout>
  
-===== Core content =====+===== 16.1 Core content =====
  
-===== Generalization of the Magnetic Field Strength =====+==== 16.1.1 Generalization of the Magnetic Field Strength ====
  
 So far, only the rotational symmetric problem of a single wire was considered in formula. I.e a current $I$ and the length $s$ of a magnetic field line around the wire was given to calculate the magnetic field strength $H$: So far, only the rotational symmetric problem of a single wire was considered in formula. I.e a current $I$ and the length $s$ of a magnetic field line around the wire was given to calculate the magnetic field strength $H$:
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Recap of the fieldline images ====+==== 16.1.2  Recap of the fieldline images ====
  
 <WRAP group><WRAP half column> <WRAP group><WRAP half column>
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 A longitudinal coil can be seen in <imgref BildNr04>. \\  A longitudinal coil can be seen in <imgref BildNr04>. \\ 
 +
 +The created field density of the coil can be derived from Ampere's Circuital Law
 +
 +\begin{align*} 
 +\theta(t) &= \int & \vec{H}(t) \cdot {\rm d}\vec{s} \\ 
 +          &= \int & \vec{H}_{\rm inner}(t) \cdot {\rm d}\vec{s} & + & \int \vec{H}_{\rm outer}(t) \cdot {\rm d} \vec{s} \\ 
 +          &= \int & \vec{H}(t) \cdot {\rm d}\vec{s}             & + &   0 \\ 
 +          &=      & {H}(t) \cdot l \\ 
 +\end{align*}
 +
 The magnetic field in a toroidal coil is often considered as homogenious in the inner volume, when the length $l$ is much larger than the diameter: $l \gg d$. \\ The magnetic field in a toroidal coil is often considered as homogenious in the inner volume, when the length $l$ is much larger than the diameter: $l \gg d$. \\
 With a given number $N$ of windings, the magnetic field strength $H$ is With a given number $N$ of windings, the magnetic field strength $H$ is
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 \end{align*} \end{align*}
 \begin{align*} \begin{align*}
-\boxed{H = {{N \cdot I}\over{l}}} \quad \quad | \quad \text{longitudinal coil}+\boxed{H = {{N \cdot I}\over{l}}}  \biggr | _\text{longitudinal coil}
 \end{align*} \end{align*}
  
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   * The major radius $R$: The distance from the center of the entire toroid (the center of the hole) to the center of the circular cross-section of the coil.   * The major radius $R$: The distance from the center of the entire toroid (the center of the hole) to the center of the circular cross-section of the coil.
 For reasons of symmetry, it shall get clear that the field lines form concentric circles. \\ For reasons of symmetry, it shall get clear that the field lines form concentric circles. \\
-Also the magnetic field strength $H$ in a toroidal coil is often considered as homogenious, when $R \gg r$.+Also the magnetic field strength $H$ in a toroidal coil is often considered as homogenious, when $R \gg r$. With a given number $N$ of windings, the magnetic field strength $H$ is
  
 \begin{align*} \begin{align*}
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 \end{align*} \end{align*}
 \begin{align*} \begin{align*}
-\boxed{H = {{N \cdot I}\over{2\pi R}}} \quad \quad | \quad \text{toroidal coil}+\boxed{H = {{N \cdot I}\over{2\pi R}}} \biggr | _\text{toroidal coil}
 \end{align*} \end{align*}
  
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-===== Common pitfalls =====+===== 16.2 Common pitfalls =====
   * ...   * ...
  
-===== Exercises =====+===== 16.3 Exercises =====
  
 <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 3.2.3 Magnetic Potential Difference"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>