Electrostatics - 1

The study of electrostatic introduces us to the vast world by electricity, magnetism, current, working of circuits and charges. Right from the attraction between a proton and neutron to the working of large high voltage generator can be explained by the simple concepts of electrostatics, the most basic of phenomenon and yet the most interesting of all.

Introduction:
Electrostatic is the study of charges that are at rest and their interactions.

Electric Charge:
It is an intrinsic property of protons and electrons, proton and electron are smallest unit of positively and negatively charge.

The S.I.unit of charge is Coulomb.

            Some properties of charges:
1)  Like charges repel while unlike attract.
2)  Charge is quantized multiple of charge on an electron.
    
3)  Net amount of charge in a system is conserved.

Coulomb’s Law:
1) Force between the two charges =
    Where r = separation between q₁ and q₂.
    And k =  where = permittivity of the medium.

    Vector form-
                        

Important points:
* Principle of superposition: Electrostatic force between any two charges is independent of other charges.
               

2) For a dielectric (insulator) medium

 Where k= dielectric constant.
            e = permittivity of the medium

Note: Electric force is an action–reaction pair and conservative in nature.

Illustration:
Two charges are placed at a distance 1.0 apart what is the minimum possible magnitude of electric force.

           

Question:

Q-1: Why
solution: Since q₁, q₂ should be minimum and q_1min = q_2min = e = C

Q-2: Five point charges of values +q are arranged on the vertices of a regular hexagon as shown in the figure, and a –q charge is placed in the center. Find the force on –q charge.

               Fig (1)

solution: Imagine two charges of   on the vacant vertex, the net force on center is now only due to -q as all other forces cancel out (principle of superposition).

                                        

                                                      Fig (2)

Electric Field:   It is the electrostatic force per unit charge.

The space around a charge where its electric force can be experienced by another charged particle.

Important points:
1)      Field due to point charge =

2)      Principle of superposition: The electric field due to multiple no of charges gets         added vectorially.

         

       Note: For continuous charge distribution

      

  Where dq is charge due to infinitesimally small element.

 

Electrical Lines of forces:
These are imaginary lines drawn to aid our visualization of properties of electric field.

Question:

Q-1: Why electric field lines never intersects?

Ans: Intersection of electric field lines implies that there are two direction of electric field at     that point which is impossible, therefore they never intersects.

Q-2: Why are electric lines always normal to the surface of a conductor?

Ans: If electric lines are not normal then there is a component along the surface which means that change of potential along the surface which is not acceptable.

Q-3: Why do electric field lines start from positive and end on negative charge?

Ans: Because the direction of electric field is from positive to negative i.e. the force on a unit positive charge is away from positive and towards negative charge.

                                                     
Field lines from +ve  Pointcharge.           Field lines towards -ve  Point charge.      

                                                                                                                           

             

          Equal +ve charge.                          Two equal but opposite charged particle