# Coloumb's Law

Coulomb’s law:

The results of many experiments done by Coulomb and many other scientists developed a relation of force exerted by a charged particle on another charge. It is given as:

$$F \propto \frac{q_1 q_2}{r^2}$$

Where $q_1$ and $q_2$ charges of the particles and r is the separation between them. We can write the above proportionality as follows:

$$F = \frac{k q_1 q_2}{r^2}$$

Where k is the proportionality constant. The vectorical representation of coulomb’s law can be written as :

$$\vec{F} = \frac{kq_1 q_2}{r^3} \vec{r}$$

When the constant value was measured experimentally it was found to be $\frac{1}{4\pi \epsilon_0}$. Where $\epsilon_0$ is the permittivity of free space, $\epsilon_0=8.85419\times 10^{-11} C^2 N{-1} m{-2}$. By substituting the constant we get:

$$F = \frac{1}{4\pi \epsilon_0} \frac{ q_1 q_2}{r^2}$$

and vectorically,

$$\vec{F} = \frac{1}{4\pi \epsilon_0} \frac{ q_1 q_2}{r^3} \vec{r}$$

### Practice problems

1. A Charge A of 5 C is placed at origin and another charge B of 5 C is placed at (5,0) on the cordinate plane. Find the electrical force acting on A and it’s direction.

2. find the force acting on B and its direction in the above question

3. Three charges of charge q are placed on the vertices of an equilateral triangle of edge a. Find the force acting on one charge because of other two charges.

4. three charges of charge q are placed on three vertices of square of side length a then find the force acting on test charge Q placed at the centre of the square.

5. by what distance two charges of charge 1C each must be separated so that force between them is equals to 50 N.

6. Two charges, 5 C and 6 C are separated by distance 1 m. At what point the third charge can be placed so that it experiences no net force.