What are Charges?

An electron is a negatively charged subatomic particle either attached to an an atom or sticks to the nucleus of the atom. Electrons exert the negative charge that tries to balance the positive charge of the nucleus.

Electric charge is the physical property of matter that causes it to exert a force when placed in an electric field or magnetic field. It is associated with the electric field and the movement of the charge produces the magnetic field that is known as the electromagnetic field. They are of protons, electrons and neutrons. The physical interaction that takes place between the charged particles experience an electromagnetic force between them which would be either attractive or repulsive in nature.  It is a scalar quantity and denoted as Q. When two currents are added the result will be an algebraic sum, although it posses magnitude and the direction of propagation.

The electric charge formula Q is:  Q= I·t

The SI unit of charge is coulomb or ampere-hour

Coulomb’s law

The magnitude of the electrostatic force which are of either attractive or repulsive between two electrically point charges at rest is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between the charges. It is also known as Electrostatic force and it is denoted as  F_e

The expression of the Electrostatic force F_e is: F_e =kq₁q₂/r² where  q₁ and  q₂are the electric charges and k is the Coulomb’s constant and r²  is the square of the magnitude of the distance between the two charges.

The Coulomb’s constant  k  is equivalent to 8.988 × 10⁹ N·m^-2/C² or 1/4πε  

An electric field is an electric property where a force is experienced within the region around a charged particle. The electric field is nothing but electric force per unit charge. They are generated by time-varying electric and magnetic fields. It is a vector quantity where the direction of the field is the direction of the force exerted on the charge.  It is denoted as E and the corresponding equation is  E=F/Q where F is the force and Q is the charge and the SI unit is Volt per meter.

Quantization of charge

The term quantization means a forceful process of constraining the input values from a large continuous, maybe infinite set of values like the real number to a discrete set or smaller set, with a finite set of values like the integer. Quantization charge means the charge can have only finite set of discrete values. The charge should be the integral multiple of the charge of an electron which is   1.6 ×10^-19 Coulombs. This phenomenon is known as Quantization of an electric charge.
The charge of a proton is  +1.6 ×10^-19 and the charge of neutron is 0.

Equation of Quantization of Charge

Let Q denote the electric charge, e denotes the charge of an electron  1.6 ×10^-19 Coulombs.

The equation of the quantization of an electric charge is:  Q=n·e where n is the integral multiple factors is which is equivalent to  n= ,1,2,3,4.. where it can be positive or negative integers, hence Q=±n·e

The primary reason to quantize the charge is that charges transfer from one to one with integral multiple of electrons and rubbing only an integral multiple of electrons can make this happen. This quantization mainly depends on the substance and is generally ignored at macroscopic levels. There isn’t any legitimate proof for this quantization but Gell-Mann and Zweig’s macroscopic element can make us understand the need and occurrence of quantization.

They have stated all of the elementary particles are made out of other elementary constituents which are known as quarks. Protons and neutrons are made up of 2 types of quarks which are UP quarks represented by ‘u’ which has a charge of  + 2e/3 and DOWN quarks represented by ‘d’ which has a charge of -e/3.

According to Gell-Mann and Zweig’s quark model, the composition of neutron (udd) has a charge of  2e/3-e/3-e/3=0 and proton (uud) has charge of 2e/3+2e/3-e/3=.e Hence this proves the quantization of charge.

Conservation of Charges

The conservation of charges states that the electric charge can neither be created nor be destroyed but is transferred from one system to another system where the total electric charge in an isolated system remains constant. The total charge of the system remains conserved. This law is intuitive since the net charge of an object will directly depend on the number of protons and neutrons. This does not imply that a system cannot produce a net charge. All the electric charges are additive and the total charge of a system is sum of all the electric charges present in the system.

Applications

1. In the process of a radioactive decay, a proton decays into a neutron and positive resulting in negligible net charge.
2. A famous experiment of using an electrically neutral glass rod when rubbed with a silk cloth, the electrons from the glass rod is transferred to the silk cloth, hence making the glass rod electron-deficient where a proton replaces its vacuum whereas the silk cloth gets negatively charged. Hence addition of positive charge and negative charge is the total charge which is 0. The net charge remains null.
3. Rubbing Amber and wool together, it gets negatively charged and when it is kept near small pieces of paper, the force exerted by the charged amber attracts the small pieces of paper.
4. Even combing the dry hair and keeping it near the small bits of paper will also attract it, since the comb gets negatively charged and exerts a strong attractive force.
5. The famous phenomenon in physics is known as the Annihilation of matter which means the reaction of a particle and its antiparticle collides and releases enormous energy. That is when electron and positron comes closer they disaster forming two γ rays. So γ=e^-+e⁺  where the net charge is zero supporting the quantization of the charge statement. 
6. To find the magnitude of the electric charge required to make 1 coulomb, quantization theorem is applied.

Total charge is denoted as Q which is 1 coulomb and the electric charge is denoted as e=1.6 × 10^-19 C

The number of electrons is n, hence applying the quantization of charge formula  Q= n·e

n=q/e

  = 1/1.6 ×10^-19

=6.25 ×10¹⁸

Therefore, 6.25 ×10¹⁸  electrons are needed to make a charge of one coulomb.

Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

• Bachelors in Science Physics
• Masters in Science Physics