## Coulomb’s Law

Coulomb’s law enables us to calculate the electrostatic force between any two point charges. It holds for distances ranging from 10^{-15} to 10^{18} m.

The force of interaction between any two point charges is directly proportional to the product of the electrical charges and inversely proportional to the square of the distance between them.

- If the charges are of same sign – force is repulsive.
- If the charges are of opposite sign – force is attractive.

\[F_{e}=\frac{K q_{1}q_{2}}{r^{2}}\]

**Unite used** **–** $q_{1},q_{2}$ are in coulomb, $F$ in newton and $r$ in metres.

$\epsilon_{o}$ is permittivity of free space,

\[\epsilon_{o}=8.854 \times 10^{-12}C^{2}/N-m^{2}\]

Dimesnsional formul of $\epsilon_{o}$ is [M^{-1}L^{-3}T^{4}A^{2}].

$K $ is a constant, its standard unit is,

\[K=\frac{1}{4 \pi \epsilon_{o}r^{2}} \simeq 9 \times 10^{9}N-m^{2}/C^{2} \]

### Important points of Coulomb’s law

- The coulomb’s law obey Newton’s third law,

\[F_{12}= -F_{21}\]

i.e. The two charges exert equal and opposite forces on each other.

- The electrical forces are conservative in nature.
- When the dielectric medium is completely filled in between charges, then the force between them decreases by a factor of dielectric constant$K$.

\[F_{\text{dielectric filled}}=\frac{F_{\text{without dielectric}}}{Kr}\times \frac{q_{1}q_{2}}{r^{2}}\]

as $\epsilon = \epsilon_{o}K$ is called permittivity of the medium,

\[F_{\text{dielectric filled}}= \frac{1}{4 \pi \epsilon} \times \frac{q_{1}q_{2}}{r^{2}}\]

- Electric force is much stronge than gravitational force.

\[F_{e}=\frac{K q_{1}q_{2}}{r^{2}}\]

and

\[F_{g}=\frac{G m_{1}m_{2}}{r^{2}}\]

as,

\[K=\simeq 9 \times 10^{9}N-m^{2}/C^{2} \]

\[G=6.67 \times 10^{-11}N-m^{2}kg^{-2}\]

Thus, $F_{e} >>F_{g}$

## Application of Coulomb’s Law

- Solving problem related to string.
- Lami’s Theorem

## Similarity between Electrostatic and Gravitational forces

- Electrostatic and Gravitational forces obey the inverse square law.
- Both are central forces.
- Both are conservative forces.

## Difference between Electrostatic and Gravitational forces

- Electrostatic forces are between two charges and gravitational forces are between two masses.
- Gravitational forces are always attractive but electrostatic forces may be attractive or repulsive.
- Electrostatic forces are 10
^{36}times stronger than gravitational forces. - Electrostatic force operates over short distances while gravitational forces operate over very large distances.