Electric Charge (ELECTROSTATS)

• It is a fundamental property like mass, length etc associated with elementary particles for example electron, proton and many more.
  
  
• Electric charge is the property responsible for electric forces which acts between nucleus and electron to bind the atom together.
  
  
• Charges are of two kinds
  (i) negative charge
  (ii) positive charge
  
  
• Electrons are negatively charged particles and protons, of which nucleus is made of, are positively charged particles. Actually nucleus is made of protons and neutrons but neutrons are uncharged particles.
  
  
• electric force between two electrons is same as electric force between two protons kept at same distance apart i. e., both set repel each other but electric force between an electron and proton placed at same distance apart is not repulsive but attractive in nature.
  
  Conclusion
  (a) Like charges repel each other
  
  
  
  (b) Unlike charges attract each other
  
  
  
  
• Assignment of negative charge on electron and positive charge on proton is purely conventional , it does not mean that charge on electron is less than that on proton.
  
  
• Importance of electric forces is that it encompasses almost each and every field associated with our life; being it matter made up of atoms or molecules in which electric charges are exactly balanced or adhesive forces of glue associated with surface tension, all are electric in nature.
  
  

Unit

• Charge on a system can be measured by comparing it with the charge on a standard body.
  
  
• SI unit of charge is Coulomb written as C.
  
  
• 1 Coulomb is the charge flowing through the wire in 1 second if the electric current in it is 1A.
  
  
• Charge on electron is -1.602 × 10 ^-19 C and charge on proton is positive of this value.

2. Basic properties of electric charge

(i) Additivity of charges

• Charges adds up like real numbers i. e., they are Scalars more clearly if any system has n number of charges q₁, q₂, q₃, q_n then total charge of the system is
  q = q₁ + q₂ + q₃ + ................ q_n
  
  
• Proper sign have to be used while adding the charges for example if
  q₁ = +1C
  q₂ = -2C
  q₃ = +4C
  then total charge of the system is
  q = q₁ + q₂ + q₃
  q = (+1) + (-2) + (+4) C
  q = (+3) C
  
  

(ii) Charge is conserved

• Charge of an isolated system is conserved.
  
  
• Chage can not be created or destroyed but charged particles can be created or destroyed.
  

(iii) Quantization of charge

• All free charges are integral multiples of a unit of charge e, where e = -1.602 × 10 ^-19 C i. e., charge on an electron or proton.
  
  
• Thus charge q on a body is always denoted by
  q = ne
  where n = any integer positive or negative
  

3. Frictional Electricity

• If we pass a comb through hairs, comb becomes electrically charged and can attract small pieces of paper.
  
  
• Many such solid materials are known which on rubbing attract light objects like light feather, bits of papers, straw etc.
  
  
• Explaination of appearance of electric charge on rubbing is simple.
  
  
• Material bodies consists of large number of electrons and protons in equal number and hence is in neutral in their normal state. But when the body is rubbed for example when a glass rod is rubbed with silk cloth, electrons are transferred from glass rod to silk cloth. The glass rod becomes positively charged and the silk cloth becomes negatively charged as it recieves extra electrons from the glass rod.
  
  
• In this case rod after rubbing, comb after passing through dry hairs becomes electrified and these are the example of frictional electricity.
  

4. Coulumb's law

• Coulomb's law is the law of forces between electric charges.
  Statement
  " It states that two stationary point charges q₁ and q₂ repel or attract each other with a force F which is directly proportional to the product of charges and inversly proportional to the square of distance between them."
  
  This dependence can be expressed by writing
  
  Fαq1q2r2
                                           (1)
  
• These forces are attractive for unlike charges and repulsive for like charges .
  
  
• We now try to express Coulomb's law in vector form for more clearity of magnitude and direction of forces.
  
  
• Consider two point charges q₁ and q₂ at points with position vector r₁ and r₂ with respect to the origin
  
  
  
  vector r₂₁= r₂ - r₁ is the difference between r₂ and r₁ and the distance of separation r is the magnitude of vector r₂₁.
  pointwise it can be written as
  r₁ = position vector of charge q₁ with respect to origin
  r₂ = position vector of charge q₂ with respect to origin
  r₂₁ = vector from 1 to 2 (r₂ - r₁)
  r₁₂ = -r₂₁ = vector from 2 to 1 (r₁ - r₂)
  r = r₁₂ = r₂₁ = distance between 1 and 2.
  
  
  
  
  Coulomb's law can then be expressed as
  
  F21=kq1q2r21r3
  $                                        (2a)
  and, F₁₂ = force on q₁ due to q₂
  
  F12=kq1q2r12r3=−F21
                                           (2b)
  

Special Case

for simplicity we can choose q₁ being placed at origin
r₁ = 0
and if we write r₂ = r the position vector of q₂ then
F₂₁ = force on q₂ due to q₁

F21=kq1q2rr3
                                         (3a)
F₁₂ = force on q₁ due to q₂

F12=−kq1q2rr3
                                         (3b)
unit vector r^ˆ₂₁ and r^ˆ₁₂ can be defined as
r^ˆ₂₁ = r₂₁/r directed from q₁ to q₂
r^ˆ₁₂ = r₁₂/r directed from q₂ to q₁ (4)
       = -r₂₁/r
force can now be written in terms of unit vector given as follows

F21=kq1q2rˆ21r2
                                         (5a)
F12=kq1q2rˆ12r2
                                         (5b)
from this we can immidiately find factors giving magnitude and the directions


• in equation (2) we find a positive constant K and experimentally found value of k is
  K = 8.98755 × 10 ⁹ Nm²/C²
  K ≅ 9 × 10 ⁹ Nm²/C²
  sometimes K is written as 1/4π ε₀ where ε₀ is the permittivity of the vaccum whose value is
  K = 1/4πε₀
  (ε₀ = 9 × 10 ^-12 C²/Nm²)