COULOMB’S LAW

Coulomb’s Law – Force between two point electric charges:

The electrostatic force of interaction (attraction or repulsion) between two point electric charges is directly proportional to the product of the charges, inversely proportional to the square of the distance between them and acts along the line joining the two charges.

Strictly speaking, Coulomb’s law applies to stationary point charges.

                                               \begin{array}{l} F \propto {q_1}{q_2}\\ F \propto \frac{1}{{{r^2}}}\\ F \propto \frac{{{q_1}{q_2}}}{{{r^2}}}\\ F = \frac{{K{q_1}{q_2}}}{{{r^2}}} \end{array}

where k is a positive constant of proportionality called electrostatic force constant or Coulomb constant.

                                              K = \frac{1}{{4\pi {\varepsilon _o}}} 

                                                     = \frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}N{m^2}/{C^2}

                        where ε0 is the permittivity of free space

              NOTE: Electrostatic Force decreases with increase in K value.

           Permitivity or Dielectric constant, K

{{\varepsilon _r} = \frac{\varepsilon }{{{\varepsilon _0}}} = \frac{{{F_0}}}{{{F_m}}}}

Where K,  is relative permitivity of the medium or dielectric constant.

(1)  When a very high electric field is created in a dielectric, the outer electron may get detached from their parent atoms. This phenomenon is known as dielectric breakdown. The minimum field at which the breakdown occurs is called dielectric strength of the material.

(2)  Material                  Dielectric Constant

      Vaccum                                         1

      GLASS                                            4

      WATER                                         80

      KERUSENE                                  2

      AIR                                                   1

Electrostatic force

Gravitational force

1.     It depends on medium between two point charges.

2.     It is valid only for point charges.

3.     Quantisation of charge (Charge on a body is an integral multiple of charge on an electron) q=+ne

4.     Charge is not concerned with Einstein’s theory of relativity.

 

 

 

 

 

 

5.     Electrostatic force may be attractive or repulsive.

6.     Electrostatic forces are extremely larger than gravitational force.

1. It does not depend on the medium between    two masses.

 2.  It is not valid for point charges

 3. Quantisation of mass in not possible.

 4. Mass is related to theory of relativity

      {m = \frac{{{m_0}}}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}}     Where m0 = Mass of the body at rest.

      m is the mass of the body moving with  velocity v. ,c is speed of light.

5. Gravitational force is always attractive.

6. Gravitational force are extremely smaller   than electrostatic force.

 

NOTE:  Electrostatic force and Gravitational force both are flow newton’s third law (action and reaction ) or both force are central force, and conservative force. 

COULOMB'S LAW IN MEDIUM

           in vacuum       {F = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{q_1}{q_2}}}{{{r^2}}}}

        {{\varepsilon _0}}= permittivity of free space  

    in medium             {F_m} = \frac{1}{{4\pi {\varepsilon _m}}}\frac{{{q_1}{q_2}}}{{{r^2}}}

         {{\varepsilon _m}}= permittivity of medium 

          {\varepsilon _r} = \frac{{{\varepsilon _m}}}{{{\varepsilon _0}}}

       {F_m} = \frac{1}{{4\pi {\varepsilon _o}{\varepsilon _r}}}\frac{{{q_1}{q_2}}}{{{r^2}}}

        {F_m} = \frac{{{F_O}}}{{{\varepsilon _R}}}

        Fm = εr Fo

        Fm  >  Fo

      coulomb force is strong 

 

Coulomb’s law in a vector form :

Where       

                       

                       

                       

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