Four electric charges $2 \mu C, Q, 4 \mu C$ and $12 \mu C$ are placed on the $x$-axis at distances $x=0, 1 \ cm, 2 \ cm$ and $4 \ cm$ respectively. If the net force acting on the charge at the origin is zero,then $Q=$ (in $\mu C$)

Two point charges $A$ and $B$ with magnitudes $+4q$ and $-4q$ are placed along a line separated by a distance $r$. The force acting between them is $F$. If $25\%$ of the charge from point $A$ is transferred to point $B$,the force between the charges now becomes:

$A$ paisa coin is made up of $Al-Mg$ alloy and weighs $0.75\,g$. It is electrically neutral and contains equal amounts of positive and negative charge of magnitude $34.8\,kC$. Suppose that these equal charges were concentrated in two point charges separated by:
$(i)$ $1\,cm$ $(\sim \frac{1}{2} \times \text{diagonal of the one paisa coin})$
$(ii)$ $100\,m$ $(\sim \text{length of a long building})$
$(iii)$ $10^6\,m$ $(\text{radius of the earth})$.
Find the force on each such point charge in each of the three cases. What do you conclude from these results?

Write the general equation for the Coulombian force on a charge ${q_1}$ due to a system of charges ${q_1}, {q_2}, \dots, {q_n}$.

Four charges are placed at the circumference of a dial clock as shown in the figure. If the clock has only an hour hand,then the resultant force on a charge $q_0$ placed at the center points in the direction which shows the time as (in $:30$)

Charges $4Q$,$q$,and $Q$ are placed along the $x$-axis at positions $x = 0$,$x = l/2$,and $x = l$,respectively. Find the value of $q$ such that the net force on charge $Q$ is zero.