Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

Link zu dieser Vergleichsansicht

Beide Seiten der vorigen Revision Vorhergehende Überarbeitung
Nächste Überarbeitung 		Vorhergehende Überarbeitung
Letzte Überarbeitung Beide Seiten der Revision
electrical_engineering_2:task_1.1.3_with_calc [2023/03/10 11:29]
mexleadmin 		electrical_engineering_2:task_1.1.3_with_calc [2023/03/15 13:38]
mexleadmin
Zeile 1: Zeile 1:
-<panel type="info" title="Task 1.1.3 Forces on Charges (exam task, ca 8% of a 60 minute exam, WS2020)"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Task 1.1.3 Forces on Charges (exam task, ca 8 % of a 60 minute exam, WS2020)"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
 <WRAP right> <WRAP right>
-{{elektrotechnik_1:coulombkraftgeometriei.jpg?400}}+{{drawio>electrical_engineering_2:coulombkraftgeometriei.svg}}
 </WRAP> </WRAP>
  
 Given is an arrangement of electric charges located in a vacuum (see picture on the right). \\ Given is an arrangement of electric charges located in a vacuum (see picture on the right). \\
 The charges have the following values:  \\ The charges have the following values:  \\
-$Q_1=7 ~\mu C$ (point charge) \\ +$Q_1=7 ~\rm{µC}$ (point charge) \\ 
-$Q_2=5 ~\mu C$ (point charge) \\ +$Q_2=5 ~\rm{µC}$ (point charge) \\ 
-$Q_3=0 ~C$ (infinitely extended surface charge)+$Q_3=0 ~\rm{C}$ (infinitely extended surface charge)
  
-$\varepsilon_0=8.854\cdot 10^{-12}  ~F/m$  , $\varepsilon_r=1$+$\varepsilon_0=8.854\cdot 10^{-12}  ~\rm{F/m}$  , $\varepsilon_r=1$
  
 1. calculate the magnitude of the force of $Q_2$ on $Q_1$, without the force effect of $Q_3$. 1. calculate the magnitude of the force of $Q_2$ on $Q_1$, without the force effect of $Q_3$.
Zeile 23: Zeile 23:
 \begin{align*} \begin{align*}
 F_C &= {{{1} \over {4\pi\cdot\varepsilon}} \cdot {{Q_1 \cdot Q_2} \over {r^2}}} \quad && | \text{with } r=\sqrt{\Delta x^2 + \Delta y^2}  \\ F_C &= {{{1} \over {4\pi\cdot\varepsilon}} \cdot {{Q_1 \cdot Q_2} \over {r^2}}} \quad && | \text{with } r=\sqrt{\Delta x^2 + \Delta y^2}  \\
-F_C &= {{{1} \over {4\pi\cdot\varepsilon}} \cdot {{Q_1 \cdot Q_2} \over {\Delta x^2 + \Delta y^2}}} \quad && | \text{Insert numerical values, read off distances: } \Delta x = 5~dm, \Delta y = 3~dm  \\ +F_C &= {{{1} \over {4\pi\cdot\varepsilon}} \cdot {{Q_1 \cdot Q_2} \over {\Delta x^2 + \Delta y^2}}} \quad && | \text{Insert numerical values, read off distances: } \Delta x = 5~\rm{dm}, \Delta y = 3~\rm{dm}  \\ 
-F_C &= {{{1} \over {4\pi\cdot 8.854\cdot 10^{-12}  ~F/m}} \cdot {{7 \cdot 10^{-6} ~C \cdot 5 \cdot 10^{-6} ~C} \over { (0.5~m)^2 + (0.2~m)^2}}} +F_C &= {{{1} \over {4\pi\cdot 8.854\cdot 10^{-12}  ~\rm{F/m}}} \cdot {{7 \cdot 10^{-6} ~\rm{C} \cdot 5 \cdot 10^{-6} ~\rm{C}} \over { (0.5~\rm{m})^2 + (0.2~\rm{m})^2}}} 
 \end{align*} \end{align*}
 </collapse> </collapse>
Zeile 30: Zeile 30:
 <button size="xs" type="link" collapse="Loesung_5_1_3_1_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_5_1_3_1_Endergebnis" collapsed="true"> <button size="xs" type="link" collapse="Loesung_5_1_3_1_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_5_1_3_1_Endergebnis" collapsed="true">
 \begin{align*} \begin{align*}
-|\vec{F}_C| = 1.084 ~N \rightarrow 1.1 ~N+|\vec{F}_C| = 1.084 ~\rm{N} \rightarrow 1.1 ~\rm{N}
 \end{align*} \end{align*}
  \\  \\
Zeile 45: Zeile 45:
 </collapse> </collapse>
  
-Now let $Q_2=0$ and the surface charge $Q_3$ be designed in such a way that a homogeneous electric field with $E_3=100 ~kV/m$ results. \\ What force (magnitude) now results on $Q_1$?+Now let $Q_2=0$ and the surface charge $Q_3$ be designed in such a way that a homogeneous electric field with $E_3=100 ~\rm{kV/m}$ results. \\ What force (magnitude) now results on $Q_1$?
  
 <button size="xs" type="link" collapse="Loesung_5_1_3_3_Tipps">{{icon>eye}} Tips for the solution</button><collapse id="Loesung_5_1_3_3_Tipps" collapsed="true"> <button size="xs" type="link" collapse="Loesung_5_1_3_3_Tipps">{{icon>eye}} Tips for the solution</button><collapse id="Loesung_5_1_3_3_Tipps" collapsed="true">
Zeile 54: Zeile 54:
 \begin{align*} \begin{align*}
 F_C &= E \cdot Q_1 \quad && | \text{Insert numerical values} \\ F_C &= E \cdot Q_1 \quad && | \text{Insert numerical values} \\
-F_C &= 100 \cdot 10^3 ~V/m \cdot 7 \cdot 10^{-6} ~C+F_C &= 100 \cdot 10^3 ~\rm{V/m} \cdot 7 \cdot 10^{-6} ~\rm{C}
 \end{align*} \end{align*}
 </collapse> </collapse>
Zeile 60: Zeile 60:
 <button size="xs" type="link" collapse="Loesung_5_1_3_3_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_5_1_3_3_Endergebnis" collapsed="true"> <button size="xs" type="link" collapse="Loesung_5_1_3_3_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_5_1_3_3_Endergebnis" collapsed="true">
 \begin{align*} \begin{align*}
- |\vec{F}_C| = 0.7 ~N + |\vec{F}_C| = 0.7 ~\rm{N} 
 \end{align*} \\ \end{align*} \\
 </collapse> </collapse>