**Coulomb’s Law**

Coulomb’s law, named after French physicist Charles-Augustin de Coulomb, describes the electrostatic interaction between two electrically charged particles.

The law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Mathematically, Coulomb’s law can be expressed as:

F = k q_{1} q_{2} / r^{2}

where F is the magnitude of the electrostatic force between the two charges, q_{1} and q_{2} are the magnitudes of the charges, r is the distance between them, and k is Coulomb’s constant, which has a value of approximately 9 × 10^{9} N·m^{2}/C^{2}.

**Some key features of Coulomb’s law include:**

- The force is proportional to the product of the charges: The greater the magnitude of the charges, the greater the electrostatic force between them.
- The force is inversely proportional to the square of the distance: As the distance between the charges increases, the force between them decreases rapidly.
- The force is attractive if the charges are opposite in sign: If the two charges are of opposite signs, the electrostatic force between them is attractive, meaning that the charges will be pulled towards each other.
- The force is repulsive if the charges are the same in sign: If the two charges are of the same sign, the electrostatic force between them is repulsive, meaning that the charges will push each other away.

## Numerical Problems Based on Coulomb’s Law for Class 12 Physics

Here we are providing numerical problems based on topic Coulomb’s Law for Class 12 Physics.

**Q.1.** Calculate coulomb force between two α-particles separated by a distance of 3.2 × 10^{-15} m in air.

(Ans. 90 N)

**Q.2.** The distance between the electron and proton in hydrogen atom is 5.3 × 10^{-11} m. Determine the magnitude of the ratio of electrostatic and gravitational force between them.

Given m_{e} = 9.1 × 10^{-31} kg, = 1.67 × 10^{-27} kg, e = 1.6 × 10^{-19} C and G = 6.67 × 10^{-11} Nm^{2} kg^{-2}

(Ans. F_{e} / F_{G} = 2.27 × 10^{39})

**Q.3. **How far apart should the two electrons be, if the force each exerts on the other is equal to the weight of the electron? Given that e = 1.6 × 10^{-19} C and m_{e} = 9.1 × 10^{-31} kg.

(Ans. 5.08 m)

**Q.4. **Two identical metallic spheres, having unequal, opposite charges are placed at a distance 0.90 m apart in air. After bringing them in contact with each other, they are again placed at the same distance apart. Now the force of repulsion between them is 0.025 N. Calculate the final charge on each of them.

(Ans. 1.5 × 10^{-6}C)

**Q.5.** Calculate the distance between two protons such that the electrical repulsive force between them is equal to the weight of either.

(Ans. 1.18 cm)