Assignment of Electrostatics

Electrostatics: The study of properties of stationary charges and devices related to these properties is called electrostatics.
     In this branch, we study about electric charges, electric forces, electric potential, capacitors etc.

Electric charge:- The property of a body due to which, it attracts or repels to another body, is called electric charge.

Types of electric charges:-
(I) Positive electric charge: When a glass rod is rubbed with silk clothe, then electric charge produced on the glass rod is called positive charge.
(II) Negative electric charge: When a plastic rod is rubbed with woolen clothe, then electric charge produced on the plastic rod is called negative charge.
This type is given by American scientist Benjamin Franklin.

Modern Principle of electrification:- When two bodies are rubbed with each other, then some electron(s) of outer most orbit of one body (whose work function is less) are transferred to the other body (whose work function is high). In this process, which body losses electrons, becomes positively charged and which body gains electrons, becomes negatively charged.

Electric induction:- When a charged body is brought near to the uncharged body, then opposite charge induces on near part and same charge induces on further part of uncharged body. This phenomenon is called electric induction.

Explanation:- when a positively charged body is brought near to the uncharged body, then free electrons of uncharged body are attracted by positively charged body. Due to this, negative charge induces on nearer part (due to majority of electrons) and same charge induces on further part (due minority of electrons) of uncharged body.
         Similarly, when a negatively charged body is brought near to the uncharged body, then free electrons of uncharged body are rappelled by negatively charged body. Due to this positive charge induces on near part (due to minority of electrons) and same charge induces on further part (due majority of electrons) of uncharged body.

Basic properties of electric charges:-

(i) Quantization of charges: The charge induced on a body is integral multiple of electronic charge e ( e = 1.6 × 10⁻¹⁹ C )
         i.e. Q = ne
Where n = number of attached or detached electrons, Q = induced charge

(ii) Conservation of charge: The total charge of an isolated system is constant. i.e. it is not possible to created or destroyed of net charge of any isolated system.

(iii) Additivity of charges: The total charge of a system is algebraic sum of all charges presented in the system.

Coulomb’s law:

(i) Like charges repel and unlike charges attract to each other.
(ii) The magnitude of electric force acting between two point charges is directly proportional to the product of magnitude of charges and inversely proportional to the square of distance between their centres.
     i.e.      F = K q₁ q₂ r²      ........... (i)
Where K is called electrostatic force constant.
In C.G.S. system of unit K = 1 and SI system K = 9 × 10⁹ N m² C⁻²
     ∴      In C.G.S. system of unit,      F = q₁ q₂ r²      ........... (ii)
And in SI system,      F = 9 × 10⁹ q₁ q₂ r²      ........... (iii)
Usually, K = 1 4πε₀ is taken
Where ε₀ is called absolute permittivity of free space. and Its value is 8.85 × 10⁻¹² C² N⁻¹ m⁻²
     ∴      F = 1 4πε₀ q₁ q₂ r²      ........... (iv)
In vector form      \(\vec{F}\) = 1 4πε₀ q₁ q₂ r² \(\hat{r}\)      ........... (iv)

Relative electrical permittivity:- The ratio of electric force between two point charges placed in vacuum to the electric force between two point charges placed in medium is called relative electrical permittivity and denoted by ε_r
     ∴      ε_r = F₀ F_m = 1 4πε₀ q₁ q₂ r² ÷ 1 4πε q₁ q₂ r² = ε ε₀

     Or      ε_r = F₀ F_m = ε ε₀ ........... (i)

     Or      ε = ε₀ ε_r

     Or      F_m = F₀ ε_r ........... (ii)

Superposition principle of electric forces:
When electric forces due to many point charges ( q₁ , q₂ , q₃ , ....... q_n ) act on a charge q₀ , then the resultant force on charge q₀ is equal to the vector sum of all remaining forces.
     i.e.      F₀ = F₀₁ + F₀₂ + F₀₃ + ........ + F_0n
Where F₀₁ = force on charge q₀ due to charge q₁
F₀₂ = force on charge q₀ due to charge q₂
F₀₃ = force on charge q₀ due to charge q₃ and so on.

Electric force between multiple point charges:

\(\vec{F_0}\) = 1 4πε₀ q₀ q₁ r₀₁² r₀₁̂ + 1 4πε₀ q₀ q₂ r₀₂² r₀₂̂ + ............. + 1 4πε₀ q₀ q_n r_0n² r_0n̂

Electric field intensity:- The electric force (Fe) per unit positive charge (q) placed in electric field of the given charge is called electric field intensity (E) at that point due to the given charge.
In scalar form      E = \(\lim\limits_{x \to 0}\) F_e q₀
In vector form      \(\vec{E}\) = \(\lim\limits_{x \to 0}\) \(\vec{F_e}\) q₀
Its SI unit is newton per coulomb or volt per meter ( N C^-1 or V m^-1 ).

Electric field intensity due to single point charge:-
In scalar form      E = k q r² = q 4πε₀ r²
In vector form      \(\vec{E}\) = = k q r² r^ = q 4πε₀ r² r^