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Exercises
Q1: Two positive charges $Q_1$ and $Q_2$ are held together by a string of length $d=10$[cm]. The first charge is $Q_1=5$[C] and the tension in the string is equal to $1.348132768\times 10^{13}$[N]. Find the value of $Q_2$.
A1: $Q_2=\frac{F_e\;d^2}{5k}=+3$[C].
Q2: Suppose that a charge $Q_1=+5$[C] is placed at the origin and a charge $Q_2=-3$[C] is placed at distance $d$[m] along the $x$ axis. There exists a point $x$ which lies somewhere between the charges $Q_1$ and $Q_2$ where the electric potential ($V$) is equal to zero. Find the value of $x$.
Hint: $V_{\text{\tiny tot}}(x)=V_1(x)+V_2(x) = \frac{kQ_1}{x} + \frac{kQ_2}{d-x}$.
Ans: $x=\frac{5}{8}d$.
Q3: Suppose that we have same situation as in the above question:
a charge $Q_1=+5$[C] is placed at the origin and a charge $Q_2=-3$[C] is placed at distance $(d,0)$[m].
Find the find the point $x$ where the strength of the electric field is equal to zero.
A3: $x=\frac{(5+\sqrt{15})}{2}d\approx 4.4365d$.
Q4: A charge $Q_1$ is placed at the origin of the coordinate system,
and a second charge $Q_2$ is placed at distance $d$[m] along the $x$ axis.
a) Find the magnitude of the electric force between $Q_1$ and $Q_2$.
b) Find the electric potential energy stored in this configuration.
c) Find the electric field $\vec{E}$ at a point $P$ which has $x$ coordinate
$x=5d$.
This point P is situated at a distance $4d$ from the charge $Q_2$.
d) Find the electric potential ($V$) at the point P.
e) If a third charge $Q_3$ is placed at the point $P$,
what will be the electric potential energy of the the configuration of the charges.
Use your answers from part b) and d) to answer this question.
A4: a) $F_e=\frac{kQ_1Q_2}{d^2}$[N],
b) $U_{12}=\frac{kQ_1Q_2}{d}$[J],
c) $\vec{E}_{\text{\tiny tot}}(P)= \vec{E}_1(P) + \vec{E}_2(P)
= \frac{kQ_1}{(5d)^2}\hat{\imath}+\frac{kQ_2}{(4d)^2}\hat{\imath}$ [N/C].
d) $V_{\text{\tiny 12}}(P) = V_1(P) + V_2(P) = \frac{kQ_1}{5d}+\frac{kQ_2}{4d}$ [V].
e) $U_{\text{\tiny tot}} = U_{12} + U_{13} + U_{23} = \frac{kQ_1Q_2}{d} + Q_3V_{\text{\tiny 12}}(P)$ [J].