electrical_engineering_2:task_1.1.5 [MEXLE Wiki]

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<panel type="info" title="Task 1.2.7 Variation: 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%>

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Given is an arrangement of electric charges located in a vacuum (see picture on the right). \\
The charges have the following values:  \\
$Q_1= 2 ~\rm{µC}$ 	(point charge) \\
$Q_2=-4 ~\rm{µC}$ 	(point charge) \\
$Q_3= 0 ~\rm{C}$ 	(infinitely extended surface charge)

$\varepsilon_0=8.854\cdot 10^{-12}  ~\rm{F/m}$  , $\varepsilon_r=1$

1. calculate the magnitude of the force of $Q_2$ on $Q_1$, without the force effect of $Q_3$.


<button size="xs" type="link" collapse="Loesung_5_1_5_1_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_5_1_5_1_Endergebnis" collapsed="true">
\begin{align*}
 |\vec{F}_C| = 0.3595 ~\rm{N} \rightarrow 0.36 ~\rm{N}
\end{align*}
 \\
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2. is this force attractive or repulsive?

<button size="xs" type="link" collapse="Loesung_5_1_5_2_Endergebnis">{{icon>eye}} Solution </button><collapse id="Loesung_5_1_5_2_Endergebnis" collapsed="true">
The force is attractive because the charges have different signs. \\ \\ \\
</collapse>

Now let $Q_2=0$ and the surface charge $Q_3$ be designed in such a way that a homogeneous electric field with $E_3=100 ~\rm{kV/m}$ results. \\ What force (magnitude) now results on $Q_1$?

<button size="xs" type="link" collapse="Loesung_5_1_5_3_Endergebnis">{{icon>eye}} Result</button><collapse id="Loesung_5_1_5_3_Endergebnis" collapsed="true">
\begin{align*}
 |\vec{F}_C| = 0.4 ~\rm{N} 
\end{align*} \\
</collapse>


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