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electrical_engineering_and_electronics_1:block17 [2025/12/02 02:10] – mexleadminelectrical_engineering_and_electronics_1:block17 [2026/01/24 15:22] (aktuell) – mexleadmin
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 ====== Block 17 — Magnetic Flux Density and Forces ====== ====== Block 17 — Magnetic Flux Density and Forces ======
  
-===== Learning objectives =====+===== 17.0 Intro ===== 
 + 
 +==== 17.0.1 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 =====+==== 17.0.2 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:
-  * ...+  * Exercise E2 Toroidal Coil 
 +  * Task 3.2.1 Magnetic Field Strength around a horizontal straight Conductor 
 +  * Task 3.3.2 Electron in Plate Capacitor with magnetic Field
  
-===== 90-minute plan =====+==== 17.0.3 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 =====+==== 17.0.4 Conceptual overview ====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - ...   - ...
 </callout> </callout>
  
-===== Core content =====+===== 17.1 Core content =====
  
 We know from [[block11]] that a static charge $Q_1$ generate a static electric field $D$. \\ We know from [[block11]] that a static charge $Q_1$ generate a static electric field $D$. \\
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-==== Definition of the Magnetic Flux Density ====+==== 17.1.1 Definition of the Magnetic Flux Density ====
  
 To derive the forces, we do a step back to the images of field lines. \\ To derive the forces, we do a step back to the images of field lines. \\
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 \begin{align*} \begin{align*}
-\boxed{|\vec{F_L}| = I \cdot |l| \cdot |B| \cdot \sin(\angle \vec{l},\vec{B} )}+\boxed{|\vec{F}_L| = I \cdot |l| \cdot |B| \cdot \sin(\angle \vec{l},\vec{B} )}
 \end{align*} \end{align*}
  
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 </callout> </callout>
  
-==== Materials ====+==== 17.1.2 Materials ====
  
 The material can be divided into different types by looking at its relative permeability. The material can be divided into different types by looking at its relative permeability.
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 \\ \\ \\ \\
 <WRAP group> <WRAP group>
-<WRAP column third>+<WRAP>
  
 === Diamagnetic Materials === === Diamagnetic Materials ===
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 </WRAP> </WRAP>
  
-</WRAP><WRAP column third>+</WRAP><WRAP >
  
 === Paramagnetic Materials === === Paramagnetic Materials ===
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 </WRAP> </WRAP>
  
-</WRAP><WRAP column third>+</WRAP><WRAP>
  
 === Ferromagnetic Materials === === Ferromagnetic Materials ===
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 </WRAP></WRAP> </WRAP></WRAP>
  
-==== Applications of the Lorentz Force ==== +==== 17.1.3 Applications of the Lorentz Force: Two parallel Conductors ===
- +
-We want to apply the Lorentz force for two common situations. +
- +
-<WRAP group><WRAP half column> +
- +
-=== Two parallel Conductors ===+
  
 The Lorentz force can be applied to two parallel conductors. \\  The Lorentz force can be applied to two parallel conductors. \\ 
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 \end{align*} \end{align*}
  
-</WRAP><WRAP half column> 
-=== Moving single Charge  === 
  
-The true Lorentz force is not the force on the whole conductor but the single force onto an (elementary) charge. \\ 
-To find this force the previous force onto a conductor can be used as a start. However, the formula will be investigated infinitesimally for small parts ${\rm d} \vec{l}$ of the conductor: 
  
-\begin{align*} +===== 17.3 Common pitfalls ===== 
-\vec{{\rm d}F}_{\rm L} = I \cdot {\rm d}\vec{l} \times \vec{B} +...
-\end{align*} +
- +
-The current is now substituted by $I = {\rm d}Q/{\rm d}t$, where ${\rm d}Q$ is the small charge packet in the length $\vec{{\rm d}l}$ of the conductor. +
- +
-\begin{align*} +
-\vec{{\rm d}F}_{\rm L} = {{{\rm d}Q}\over{{\rm d}t}} \cdot {\rm d}\vec{l} \times \vec{B} +
-\end{align*} +
- +
-Mathematically not quite correct, but in a physical way true the following rearrangement can be done: +
- +
-\begin{align*} +
-\vec{{\rm d}F}_{\rm L} &= {{{\rm d}Q \cdot   {\rm d}\vec{l}}\over{{\rm d}t}} \times \vec{B} \\ +
-                       &= {\rm d}Q   \cdot {{{\rm d}\vec{l}}\over{{\rm d}t}} \times \vec{B} \\ +
-                       &= {\rm d}Q   \cdot {{{\rm d}\vec{l}}\over{{\rm d}t}} \times \vec{B} \\ +
-\end{align*} +
- +
-Here, the part ${{{\rm d}\vec{l}}\over{{\rm d}t}}$ represents the speed $\vec{v}$ of the small charge packet ${\rm d}Q$. +
- +
-\begin{align*} +
-\vec{{\rm d}F}_{\rm L} &= {\rm d}Q \cdot \vec{v} \times \vec{B}  +
-\end{align*} +
- +
-The **Lorenz Force** on a finite charge packet is the integration: +
- +
-\begin{align*} +
-\boxed{\vec{F}_{\rm L} = Q \cdot \vec{v} \times \vec{B}} +
-\end{align*} +
- +
- +
- +
-<callout icon="fa fa-exclamation" color="red" title="Notice:"> +
- +
-  * A charge $Q$ moving with a velocity $\vec{v}$ in a magnetic field $\vec{B}$ experiences a force of $\vec{F_{\rm L}}$. +
-  * The direction of the force is given by the right-hand rule. +
- +
-</callout> +
- +
-</WRAP></WRAP> +
- +
- +
-===== Common pitfalls ===== +
-  * ...+
  
-===== Exercises =====+===== 17.4 Exercises =====
  
 {{page>electrical_engineering_and_electronics:task_0j7accfimmemytq9_with_calculation&nofooter}} {{page>electrical_engineering_and_electronics:task_0j7accfimmemytq9_with_calculation&nofooter}}
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 #@HiddenEnd_HTML~202,Result~@# #@HiddenEnd_HTML~202,Result~@#
  
 +</WRAP></WRAP></panel>
  
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 ===== Embedded resources ===== ===== Embedded resources =====
 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. 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.
 +\\ \\ \\
 +<WRAP column half>
 +The rotating flux (density) in the stator of a motor, source/CC-BY 3.0 see {{https://commons.wikimedia.org/wiki/File:2HP_1500RPM_induction_motor_no_slip.gif|wikipedia}}
 +{{electrical_engineering_and_electronics_1:2hp_1500rpm_induction_motor_no_slip.gif}}
 +</WRAP>
  
- +<WRAP column half> 
-A living insect ("diamagnet") floats in a very strong magnetic field+A living insect ("diamagnet") floats in a very strong magnetic field \\
 {{youtube>KlJsVqc0ywM?start=45}} {{youtube>KlJsVqc0ywM?start=45}}
 +</WRAP>
  
 \\ \\ \\ \\
-Explanation of diamagnetism and paramagnetism +<WRAP column half> 
-<WRAP> +Explanation of diamagnetism and paramagnetism \\ 
-<WRAP column half>{{ youtube>u36QpPvEh2c }}         </WRAP> +{{ youtube>u36QpPvEh2c }}         
-<WRAP column half>{{ youtube>pniES3kKHvY?300x500 }} </WRAP>+
 </WRAP> </WRAP>
 +<WRAP column half>
 +In Oxygen magnetic? \\
 +{{ youtube>pniES3kKHvY?300x500 }} 
 +</WRAP>
 +
  
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