### COULUMB’S LAW

The first quantitative measurements of electric force between point charge bodies was made by Charles Augustin de Coloumb in 1785 by means of a very sensitive balance (torsion balance).

**It states that the magnitude of force between two point charges is directly proportional to the product of two charges and inversely proportional to the square of the distance between them**.”

Let q_{1} and q_{2} be the two charges separated by a distance r in vacuum.

Where K is the proportionality constant.

where = absolute permittivity of free space =

**∴ **

**In any medium, force is**:

Where is called relative permittivity of the dielectric medium or dielectric constant.

**Note: **

(a) **Coulomb’s law hold good only for stationary charges**.

(b) It hold good for **point charges** only i.e their linear dimension are much smaller than the distance.

(c) **It is a central force** i.e the force will act along the line joining the centres of two charged bodies.

(d) **It is a conservative force.**

(e) If q_{1}q_{2} > 0, i.e like charges **∴** repel each other.

If q_{1}q_{2} < 0, i.e unlike charges **∴** attract each other.

(f) If charges are placed in any other medium then .

(g) The variation of electrostatic force with respect to (for q_{1}q_{2} > 0 and q_{1}q_{2 }< 0) is as shown in the graph.

(h) The variation of force with respect to distance r is as shown in the graph.

(i) **The electrostatic force between two charges is spherically symmetric**.

(j) Electrostatic force between two charges is not affected by the presence of other charges. Hence electrostatic force is a two body interaction.

(k) Dimension of

$latex \displaystyle \,\,\,=\frac{\left[ AT \right]\left[ AT \right]}{\left[ ML{{T}^{-2}} \right]\left[ {{L}^{2}} \right]}=\frac{\left[ {{A}^{2}}{{T}^{2}} \right]}{\left[ M{{L}^{3}}{{T}^{-2}} \right]}=\left[ {{M}^{-1}}{{L}^{-3}}{{T}^{4}}{{A}^{2}} \right]$

**COULOMB’S LAW IN VECTOR FORM:**

Consider two point charges q_{1} and q_{2} are kept apart by a distance r in vacuum or air.

$latex {{\overrightarrow{F}}_{12}}$ = force on (1) due to (2)

$latex \displaystyle {{\overrightarrow{F}}_{12}}\,=\,K\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}.{{\widehat{r}}_{21}}$ [Here is a unit vector pointing from q_{2} to q_{1}].

Similarly, $latex \displaystyle {{\overrightarrow{F}}_{21}}\,=\,K\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}.{{\widehat{r}}_{12}}$ [Here is a unit vector pointing from q_{1} to q_{2}].

Since

**∴ ** $latex {{\overrightarrow{F}}_{12}}\,=\,-{{\overrightarrow{F}}_{21}}$

Thus the force extended by two charges on each other is equal and opposite i.e., they obey Newton’s third law of motion.

**DEFINITION OF 1 COULOMB:**

We have,

If q_{1} = q_{2} = 1 C, r = 1m and ,

Then F = K = 9 x 10^{9} N

“Thus one coulomb is that quantity of charge which exerts a force of 9 x 10^{9} N on each other when kept apart 1m in vacuum.

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