Coulomb's Law - Practice Questions & MCQ

Coulomb's Law: The force of attraction or repulsion between two charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.

$
\begin{aligned}
& F \propto \frac{Q_1 Q_2}{r^2} \\
& F=\frac{K Q_1 Q_2}{r^2}
\end{aligned}
$

$\mathrm{K}=$ Proportionality Constant
$Q_1$ and $Q_2$ are two Point charges
In SI unit value of K is

$
K=\frac{1}{4 \pi \varepsilon_0}
$

Where,

$
\left(\varepsilon_0\right)=8.85 \times 10^{-12} \frac{C^2}{N-m^2} \text { known as absolute permittivity of air or free }
$

space

The vector form of Coulomb's Law: 

Consider two charges $q_1$ and $q_2$ separated by a distance r. Let the position vectors of $q_1$ be $r_1$ and that of $q_2$ be $r_2$. Then the force due to $q_2$ on $q_1$ as shown in figure $F_{12}$ is directed along the unit vector $r_{12}$ and

$
\begin{aligned}
& F_{12}=\frac{K q_1 q_2}{r^2} \hat{r}_{12} \\
& \text { here, } \hat{r}_{12}=\frac{\vec{r}_1-\vec{r}_2}{\left|r_1-r_2\right|}=\frac{\vec{r}_{12}}{r} \\
& F_{12}=\frac{K q_1 \cdot q_2}{r^3} \vec{r}_{12}
\end{aligned}
$

Force when dielectric inserted between the charges:
When a dielectric of dielectric constant $k$ is completely filled between the charges then force

$
F_{\text {med }}=\frac{q_1 q_2}{4 \pi \varepsilon_0 k r^2}=\frac{q_1 q_2}{4 \pi \varepsilon_0 \epsilon_r r^2}
$

$\epsilon_r$ is relative permittivity / dielectric constant of the medium. The dielectric constant is the ratio of the permittivity of a substance to the permittivity of free space. (dielectric will be explained later in detail in this chapter)

If the dielectric of thickness d is partially filled between the charges $Q_1$ and $Q_2$ then

                                                                            $F=\frac{Q_1 Q_2}{4 \pi \epsilon_0(r-d+\sqrt{k} d)^2}$

Principle of Superposition:

It states that the total force acting on a given charge due to a number of charges is the Vector sum of the individual forces acting on that charge due to all the charges.