Task 1.2.7 Variation: Forces on Charges (exam task, ca 8% of a 60 minute exam, WS2020)
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 $Q_3$.
\begin{align*}
|\vec{F}_C| = 0.3595 ~\rm{N} \rightarrow 0.36 ~\rm{N}
\end{align*}
2. is this force attractive or repulsive?
The force is attractive because the charges have different signs.
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 $Q_1$?
\begin{align*}
|\vec{F}_C| = 0.4 ~\rm{N}
\end{align*}