Task 1.2.5 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:
$Q_1=7 ~\rm{µC}$ (point charge)
$Q_2=5 ~\rm{µC}$ (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 $Q_3$.
- Which equation is to be used for the force effect of charges?
- How can the distance between the two charges be determined?
\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 {\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} ~\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*}
\begin{align*}
|\vec{F}_C| = 1.084 ~\rm{N} \rightarrow 1.1 ~\rm{N}
\end{align*}
2. is this force attractive or repulsive?
- What force effect do equally or oppositely charged bodies exhibit on each other?
The force is repulsive because both charges have the same sign.
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 $Q_1$?
- Which equation is to be applied for the force action in the homogeneous field?
\begin{align*}
F_C &= E \cdot Q_1 \quad && | \text{Insert numerical values} \\
F_C &= 100 \cdot 10^3 ~\rm{V/m} \cdot 7 \cdot 10^{-6} ~\rm{C}
\end{align*}
\begin{align*}
|\vec{F}_C| = 0.7 ~\rm{N}
\end{align*}