3.0 Coulomb's law

  Electrostatics

Coulomb's law was discovered by Charles Augustin de Coulomb in the year 1785.

Coulomb's law describes how static charges interact with one another.

Coulomb's law stated that the electrostatic force between two stationary charges is proportional to the product of magnitude of charges and inversely proportional to the square of the distance between them.

Mathematically, $$F \propto \frac{{{q_1}{q_2}}}{{{r^2}}}$$ or $$F = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{q_1}{q_2}}}{{{r^2}}}$$ or $$F = \frac{{k{q_1}{q_2}}}{{{r^2}}}$$
Also for simplicity we can write, $$\frac{1}{{4\pi {\varepsilon _0}}} = k = 9 \times {10^9}N{m^2}{C^{ - 2}}$$
where,

${q_1}\,\& \,{q_2}:$ Charges on the particles
$r:$ Distance between the charges
$F = 9 \times {10^9}N{m^2}{C^{ - 2}}:$ Proportionality constant
${\varepsilon _0} = 8.854 \times {10^{ - 12}}{C^2}{N^{ - 1}}{m^{ - 2}}:$ Permittivity of free space

Note:

• The force is attractive if the charges are of opposite signs and is repulsive if they are of the same sign.
  
  
• The above equation of Coulomb's law can be used for point charges in the vacuum only.
  
  
• The Coulomb's force between two charged in a medium is, $$F_{\text{medium}} = \frac{1}{{4\pi {\varepsilon _r}}}\frac{{{q_1}{q_2}}}{{{r^2}}}$$ or $$F = \frac{1}{{4\pi {\varepsilon _0}K}}\frac{{{q_1}{q_2}}}{{{r^2}}}$$
  where $${{\varepsilon _r} = {\varepsilon _0}K}$$ is called permittivity of the medium.
  $${F_{{\text{medium}}}} = \frac{{{F_{{\text{vacuum}}}}}}{K}$$
  
  
• The electrostatic force is an action-reaction pair, i.e., the two charges exert equal and opposite forces on each other.
  $${F_{AB}} = {F_{BA}}$$