Electric Charges and Forces - Coulomb's Law - Polarization

The modern picture of an atom is a nucleus which is very small compared to the size of the atom.And if the atom is neutral the number of electrons and the number of protons is the same.If you take electron off you get a positive ion.If you add an elentron then you get a negative ion. The charge of the electron is the same as the charge of the proton.That's why the number is the same for neutral  atoms. 

Electrostatics deals with forces between charges.  Static means the charges are not moving, or at least a re not moving very fast. 

How fast is "not very fast"? 
When a charge moves, it generates a magnetic field, which can lead to a magnetic force. As we begin our study of electricity, we want to minimize complexity and focus just on electric force. To keep things simple, we let charges stand still, or move very slowly. So "not very fast" means motion so slow the magnetic effects are insignificant compared to the electric forces. 

Charge 

The concept of charge arises from an observation of nature: We observe forces between objects. Electric charge is the property of objects that gives rise to this observed force. Like gravity, electric force "acts at a distance". The idea that a force can "act at a distance" is pretty mind-blowing, but it's what nature really does.Electric forces are very large, far greater than the force of gravity. Unlike gravity, there are two types of electric charge, (whereas there is only one type of gravity; gravity only attracts). 

Consider a system of two point charges, q1 and q2,  separated by a distance r in vacuum. The force exerted by q1 on  q2 is given by Coulomb's law: 

Note that electric force is a vector which has both magnitude and direction. In SI units, the Coulomb constant Ke is given by

Where

is known as the “permittivity of free space.” Similarly, the force on q1​​ due q2​​ to  is given by

The modern picture of an atom is a nucleus which is very small compared to the size of the atom.And if the atom is neutral the number of electrons and the number of protons is the same.If you take electron off you get a positive ion.If you add an elentron then you get a negative ion.

The charge of the electron is the same as the charge of the proton.That's why the number is the same for neutral  atoms.

Electrostatics deals with forces between charges.  Static means the charges are not moving, or at least are not moving very fast.
How fast is "not very fast"?
When a charge moves, it generates a magnetic field, which can lead to a magnetic force. As we begin our study of electricity, we want to minimize complexity and focus just on electric force. To keep things simple, we let charges stand still, or move very slowly. So "not very fast" means motion so slow the magnetic effects are insignificant compared to the electric forces.
Charge
The concept of charge arises from an observation of nature: We observe forces between objects. Electric charge is the property of objects that gives rise to this observed force. Like gravity, electric force "acts at a distance". The idea that a force can "act at a distance" is pretty mind-blowing, but it's what nature really does.Electric forces are very large, far greater than the force of gravity. Unlike gravity, there are two types of electric charge, (whereas there is only one type of gravity; gravity only attracts).

Force between charges: Coulomb's Law of electric force
Coulomb's Law very nicely describes this natural phenomenon. The law has this form,

The Electric Constant, ϵ 0 \epsilon_0 ϵ 0 ​ \epsilon, start subscript, 0, end subscript , the permittivity of free space

K, the constant of proportionnality , frequently appears in this form,

Coulomb's Law describes something that happens in nature. The electric constant, ϵ 0 \epsilon_0 ϵ0​\epsilon, start subscript, 0, end subscript, describes the experimental setup and the system of units. "Experimental conditions" refers measuring F ⃗ \vec F F F, with, vector, on top on point charges (or something that acts like a point charge, like charged spheres). In the SI system of units, ϵ 0 {\epsilon_0} ϵ0​\epsilon, start subscript, 0, end subscript is experimentally measured to be,    

ϵ0​=8.854187817×10−12\epsilon, start subscript, 0, end subscript, equals, 8, point, 854187817, times, 10, start superscript, −, 12, end superscript coulomb 2 / ^2/ 2/squared, slash newton-meter 2 ^2 2

This value of make, K=4πϵ0​1​=4π⋅8.854×10−121​=9×109

The dimensions of K K KK are: newton-meter 2 / ^2/ 2/squared, slash coulomb 2 ^2 2squared .