Coulomb's Law 

Another name of coulomb's law is Inverse square law. 

In this article we discuss about 
1. Coulomb's law of electrostatic : statement 
2. Coulomb's law of electrostatic in vector form 
3.Coulomb's law of electrostatic in scalar form 
4. Coulomb's law constant 
5. Coulomb's law example and questions 
6. Comparison between electrostatic force and gravitational force 
7. Some observations about Coulomb's interaction 

    We have seen that same charge repel each other and opposite charge attract each other. The force between the two charges is given by Coulomb's law of electrostatic.
This is an analogue of Newton's law of gravitation.  

Statement of Coulomb's law of electrostatic 

This law states that the force of attraction or repulsion between the two charges separated by a distance 'r' is directly proportional to the product of two charges and inversely proportional to square of distance between them.
Coulomb's law of electrostatic
Let q1 and q2 are two electric charge. Distance between them is 'r'.
       proportional to q1q2
       inversely proportional to r'2(square of r) 
      So, F proportional to q1q2/ square of r
  We can write 
Coulomb's law

Where 'k' is proportionality constant.
   This force also depends upon the nature of intervening medium. It acts along the line joining two charges. 
         This form of Coulomb's law known as Coulomb's law of electrostatic in scalar form.  

Coulomb's law constant 

'k' the proportionality constant is called Coulomb's law constant. 
     Value of k is depends on the nature of the medium in which two charges are situated. It also depends upon unit in which the quantity F, q1, q2 and r are measured. 
   Here k= 1/K
In SI system -   
    Here k = 1/ 4(pi)€o€r.    (€ is epsilon) 
Where €o is permitivity of free space (vacuum) and €r is the relative permitivity of given medium. 
        Relative permitivity of a medium is defined as the ratio between absolute permitivity(€) of the medium and absolute permitivity of free space (€o). 
     €r = €/€o

the value of K for free space is 
Coulomb's law constant
€o= permitivity in free space
Permitivity
    Value is =8.854×10'(-12)
  Dimension of €o , in mass, length, time and current are -1,-3,4 and 2 respectively. 
Now Force will be
Coulomb's law
In CGS system -
     In electrostatic system of unit (e.s.u)
               k= 1/K
  Where K is called as dielectric constant of the medium which is taken to be equal to the value of K is 1 for free space (vacuum) 
     Therefore
Force in space 
        F=q1q2/ r²
Force in any medium 
       F = (1/K) q1q2/r²

Coulomb's law of electrostatic  in vector form 

      To discuss Coulomb's law in vector form, we used some notation which are given below 
    F12 = Force acting on charge q1 due                                                          to q2 
F21 = Force acting on charge q1 due to                                                                q2 
     r12 = displacement from charge q1 to q2
     r21 = displacement from charge q2 to q1 
    Here all are in vector form. 

When both charges are similar in nature, force between them is repulsive in nature. 
   Here F12  and F21  are in opposite direction. 
 In vector form force can be 
Coulomb's law in vector form
And  another is 
Coulomb law in vector form

     This is the two forces opposite to each other. 
     For unlike charge we can also calculate force in vector form. 

  From that we can find whenever two charge are facing each other, they experience equal and opposite force. 
The appearance of charge Coulomb's law

Application of Coulomb's law of electrostatic 

Coulomb's law 's fundamental use in the preparation of electroscope. 
-  Coulomb's law of electrostatic help us to calculate electric field of charge. 
-  Coulomb's law help us to find force between two charges. 

Electroscope

  Dielectric constant (K) 

      Consider two charges q1 and q2 placed at a distance r from each other. If F1 and F2 are the magnitude of force between them in free space and the in a medium respectively. Then 
  In e.s.u 
We get F1 /F2  = K 
 Which is the dielectric constant of the medium. 
  In SI unit 
We get     F1 /F2  = €/€o = €r 
  Which is the relative permitivity of the medium. 
   Hence, K = €r
  So, the dielectric constant K of a medium can beat defined as the ratio of the forge between two charges separated by some distance apart in free space to the force veteran the same two charges separates by the same distance apart in that medium. Thus K dimension less. 
 

     Some observations about Coulomb's law of interaction 

    Interaction of two charges with each other is known as Coulomb interaction and the who explain the force between the two charges is called Coulomb's law. 
The observations are 
1. Coulomb obtain this law by studying experimentally. So we can say it is a experimental law. 
2. This law is stricktly applicable for point charge. If a charge body have negligence of dimension then we can say charge is a point charge. 
3. Coulomb's force between the two charges or charge body is mutual interaction. 
4. Coulomb's interaction is not affected by presence of any other charges around the observed charge. 
5. We can apply Coulomb's law when the charges are at rest condition. And when we apply it in case of motion its need modification. 
6. Coulomb's force is attracted in nature in case of dissimilar charges . 
7. The magnitude of force depends upon the charge of the body, separation between them and nature of medium. 
8. The direction of force depends upon the relative orientation of charge. 
9. Coulomb's force is a central force. 
10. Coulomb's force is conservative in nature. Thus ,work done in moving a charge, under the effect of Coulomb's force, is independent of path followed. 

    Coulomb's law of electrostatic is not  always valid 
 Coulomb's law is strictly applicable for point charges. 
  Point charges - these are the charged body which size are very small as compare to interaction distance.

   Now we discuss about invalid of Coulomb's law. 
  Let us consider two charged bodies which have charges q1 and q2. They are separated by a distance of 3 light year. 
    Here the charged particles are in their position from a long time, so now we can calculate the force on them according to Coulomb's law. 
     But if we move charge q2 by a small distance dx towards  q1 , then according to Coulomb's law force on both charged particle will increase at that instant . 
      But we know that according to theory of relativity no information can travel by lager speed than speed of light . 
     So here the information of changing of particle position will take 3 years to travel from q2 to q1. For this time period Coulomb's law is not valid. 
    But if we explain this phenomenon in terms of electric field it will valid. 

For better understanding check out this video of hc verma (this lacture is in Hindi) 


Comparison between electrostatic force and gravitational force 
 Similarity
1. Both electrostatic force and gravitational force obey the inverse square law. 
2. Both of these forces are central force. 
3. Both of these force are conservative force. It means work done in their cases is independent of the path followed. 
4. Born of those force operate in vacuum. 

   Dissimilarity
1. Electrostatic force may be attractive or repulsive in nature but gravitational force is attractive in nature. 
2. Electrostatic force are strong force while electrostatic force is weak force. 
Some conceptual questions on Coulomb's law of electrostatic 

1. Why is electrostatic so named? 
  Answer: It is so named because it deals with the charge at rest. 

2. Is force of attraction between two charges is a central force? 
 Answer :  Yes,  it is a central force since it is directed along the line joining the two charges and is a function of separation between them. 

3. How many line of force start from a unit charge? 
 Answer :  4(pi)  lines of force 

4. Can two conductor, having same nature of charge on them, attract each other? 
Answer :  Yes they can do so if the charge one of them is much larger than the other. In that case the charge induced in the second body is much larger. 
     This induced charge produces a resultant charge of opposite nature after neutralising the original charge on second body. After neutralising the two bodies carry opposite charges and hence attract each other. 

5. A table tennis ball is covered with a conducting paint and is suspended in between two plates. One plate is connected to a source of high potential while the other is earthed. Describe the behaviour of the ball. 
  Answer :   The ball will be attracted towards the charge plate, say positive, because of the induction on ball. It strikes against the plate and gets charged positively. 
       It moves away from first plate towards second, strikes against it and get neutralised. This process is repeated on and on. Thus, the ball will oscillate like a pendulum in between two plates.  

6. Two identical metal sphere of exactly equal mass are taken. One is given a positive charge of q coulomb and the other an equal negative charge. Are their masses, after changing equal ?
 Answer :  A body is positively charge due to extraction of electrons from it while it becomes negatively charged due to addition of electrons into it. Thus, after charging, the negatively charged sphere will have a slightly greater mass. 

7. A comb after going through a dry hair is able to attract small bits of paper towards it. Why is it so ?
     Answer :   Comb, while working through dry hair, gets charged due to friction between comb and hair. As this charged comb is brought near a bit of paper in induces a charge of opposite nature on the nearer end of the paper. This result in attraction between comb and paper. 

8. A positively charged body attracts a pitch ball pendulum towards it. Does it mean that the pitch ball pendulum is negatively charged  ?
Answer :        Not  nessery , a positive charged body can induced negative charge on the near end of uncharged ball ,thus, causing an attraction between them. 

9. Vehicles carrying highly inflammable material have chains to the ground. Why is it so  ?
  Answer :      While moving through air at high speed, the body of the vehicle get charged. The chains hanging to the ground convey this charge to earth ,thus, without producing any possible harm to the inflammable material. 

10. A light uncharged metal sphere suspended from a thread is attracted towards a charged glass rod. After touching the rod, the sphere is repealed by the rod . Explain  ?
      Answer :     The charged glass rod, when brought nearer the metal sphere, induces charge of opposite nature on the nearer end of the sphere. Therefore, the sphere is attracted towards the rod. On touching ,some some of the charge from the rod is transferred on the sphere. Then there will be a repulsion between the two charged bodies as the two carry similar type of charge. 

11. Why line of force so named ?
    Answer :          A unit positive charge, when placed in an electric field, experience a force. If free, it would move under the action of this force. Therefore, path of motion of unit positive charge is called line of force. 

Coulomb's law example 

1. Two equal and similar charge 0.003 m apart, in air, repel each other with a force of 4.5 kg f. Find the charge in coulomb  ?
  Hints for solution : 
Here force F = 4.5 kg f = 4.5×9.8 N
      Charge is given 
                              q1 = q2 = q 
    Distance between them is 0.003m
By applying Coulomb's law we can calculate value of charge. 

2. In hydrogen atom the electrical force of attraction between the electron and proton is 8.1×10'(-8) N  [ here ' means to the power ] . Calculate the distance between the electron and proton. Given : charge on electron is 
1.6×10'(-19) .
     Hints for solution : 
  Here charge is given that is q1 and q2 is known as charge particle are electron and proton. 
    Force between them is given 
  We have to calculate distance between them by applying Coulomb's law of electrostatic. 

3. Two charges Q and Q are placed at  the diagonally opposite corners of a square while charges q and q are placed at the remaining corners. If the resultant force on the charge Q is zero, find the relationships between Q and q. 
Hint for solution : 
       First calculate force on Q by another three charges by applying Coulomb's law. 
Here we find three force take resultant of two forces and and with third force to get resultant force on Q. 
    The equation are appear like 
    F' = (F1 ² + F2 ² )½
After calculating 
    We can write F + F' =0 
Here F is force acting on Q along the direction of diagonal. 
      By solving the above equation we will get result as   Q = -2(2)½q 
                   It means        ( 2 × root 2 )

4. Calculate the force between two charges having charge 2 C and 5C. Separation between them is 10 cm. Calculate force between them ?
Hints for solution : 
      Here convert all unit in SI system then calculate force by applying Coulomb's law of electrostatic. 


       
     

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This is all about state and explain Coulomb's law of electrostatic . If you have any queries you can ask in comment box. 
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