Coulombs law , electric charges and electric fields. It is very important for you to know about this. If you are preparing for JEE, NEET, IIT or any other exam.
Because questions are often ask from here. If you want to know and understand well, then you have to read the information given here carefully and completely.
So first you need to know what is this electric charge. Let us know what is electric charge?
See also this : Electric lines of force properties
What is electric charge?
Charge is a fundamental characteristic of elementary particles of matter. which can describe or explain some interactions and some types of interactions energies and the physical quantity of electric charge is scalar quantity.
And electric charges are two types
- Positive charge &
- Negative charge.
1. Positive charge
When we rub a glass rod with silk, the kind of charges that the glass rod acquires is called positive charge.
2. Negative charge
- When we rub amber with woolen cloth , the kind of charge that the amber acquires is called negative charge.
Characteristics of electric charge
We have learned that there are two types of electric charge, one positive and one negative. Which has been described above, it has the following characteristics.
The following characteristics are
- Discrete nature of charge or quantisation of charge.
- Conservation of charge.
- Additive nature of charge.
- Invariance of charge.
1. Discrete nature of charge or quantisation of charge.
If a body carries a charge, then the charge carried by that body is not continuous but the discrete nature of charge is an integral multiple of some smallest unit of charge.
The charge of an electron is denoted by the smallest unit of charge, e– , and its magnitude is equal to 1.6×10-19 coulomb.
The charge carried by some other body will be equal to ±ne , where n = 1,2,3,4,5 etc. Therefore, the charges are said to be of discrete(discontinuous) nature or it is also called quantized.
2. Conservation of charge
According to conservation of charge, the total charge in an isolated system remains constant, and total charge means the algebraic sum of positive and negative charges.
3. Additive nature of charge
If the total charge on an extended body is equal to the algebraic sum of the charges located at different points or in different regions of the body, then it is called additive nature of charge.
4. Invariance of charge
If change from one inertial frame of reference to another inertial frame of reference, the amount of that charge remains the same.
Mechanism of electrification by friction-
Suppose there are two substances, ‘A’ and ‘B’. When substance ‘A’ is rubbed with substance ‘B’, some electrons from the atoms or molecules of substance ‘A’ will be separated from the electronic cloud and transferred to substance ‘B’.
But substance ‘B’ can acquire negative charge in the same amount as will be discharged by substance ‘A’ , and we can say that both substance A and substance B are charged.
- Ebonite
- Celluloid
- Rubber
- Sulphur
- Metals
- Resin
- Amber
- Wood
- Cotton
- Silk
- Wool
- Mica
- Glass
- Flannel
- Fur
Thus, the material occurring first will be positively charge and the material occurring later will be negatively charge.
What is Coulombs law in scalar form
Coulomb’s law in scalar form states that the electrostatic force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between the two bodies.
and
inverse square law ,
Combining,
or
Where β is a constant of proportionality that depends on the nature of the medium in which the two charges are located. It also depends on the units in which the quantities F, q1 , q2 , and r are measured.
What is Coulombs law in vector form
Consider two point charges q1 and q2 which lie at A and B respectively. Then , suppose 
and be the position vectors of A and B with respect to reference points O.
But according to Coulomb’s law, the force 
exerted by q1 charge and q1 is –
Where 
is a vector and it is a unit vector along 
. The force is , thus repulsive in nature.
And an isolated system is a system in which no matter passes through.
As
or
Applying triangle’s law of vector addition in ΔOAB,
, ∴ 
Similarly, force [ in figure No-1(b)] on charge q1 by q2 is given by
From both equations (1) and (2),
In Special case – In case one of the charges , say q1 , is situate on the origin. (See figure , No-2 )
and 
For acting on charge q2 due to charge q1 is given by
or 
Where 
is the unit vector in the direction of 
.
Importance of Coulomb’s law in vector form
Importance of Coulomb’s law in vector form , as we know 
Because 
, Hence Coulombian force obey newton’s third law of motion.
And coulomb’s force acts along , so these are the central force.
One thing to remember always , coulomb’s force is long range force and it having infinite charge. If F = positive charge then , the force is repulsive and if F = negative charge then the force is attractive.
Derivation of coulomb’s law in vector form
and the force of the q2 charge is . And the direction of the two charges is 
for q1 and for q2 .Now let’s derive it,
Then, we can also write this
And will be
So here it is, some important information regarding Coulombs law, electric charge and electric field. If you need any more information related to this, then tell us by commenting.