Unit-1 ELECTROSTATICS

Coulomb’s law:

Coulomb’s law states that the force ‘F’ between two point charges Q₁ & Q₂ is directly proportional to the product of two charges and inversely proportional to the square of the distance ‘R’ between them and is along the line joining them.

F = K.Q₁.Q₂ / R²

Where ‘K’ is a proportionality constant whose value depends on the system of units.

Q₁ & Q₂ are in coulomb’s(c), ‘R’ is the distance in meters(m) and force in ‘N’.

K =

Where ε₀ is called the permittivity of free space and Q1

ε₀= 8.85* 10^-12 F/m or K=

= 9*10⁹ m/F r1 R

F =

. Q₁.Q₂/ R^{2 Q2}

If point charges Q1 & Q2 are located at points having position vectors o

r1 & r2 then the force F₁₂ = Q1.Q2.a_r12 / 4πε₀.R²

Where R₁₂ = r2 – r1 ; R = |R₁₂| ; a_r12 = R₁₂/ R

F₁₂ = Q1.Q2(r2-r1)/ 4πε₀|r2-r1|³

Similarly force F₁₂ on Q1 due to Q2 , which is same in magnitude but opposite in direction, i.e,

F₂₁ = -F₁₂ ; F₂₁ = |F₁₂|a_r21 = |F₁₂|(-a_r12) i.e., a_r21 = -a_r12

Coulomb’s law of point charges is applicable when the distance ‘R’ between Q1 & Q2 must be large when compared to linear dimensions of the charges i.e. Q1 & Q2 must be point charges.

If there are more than two point charges i.e. if there are ‘N’ charges then the principle of superposition of charges is applied. It states that if there are ‘N’ charges Q1,Q2,……Qn located at positions r1,r2,…….rn, then the resultant force ‘F’ is given by , sum of the forces exerted on Q be each of the charges Q1,Q2,…….Qn.

F =

Electric field intensity (EFI):

It is defined as the force per unit charge when placed in an electric field.

E = F/Q

For Q>0 , the electric field intensity ‘E’ is obviously in the direction of the force ‘F’ and is measured in newtons per coulomb or volts per meter. The electric field intensity at a point ‘r’ due to a point charge located at ‘r^|’ is given by

E = Q.a_r / 4πε₀.R² = Q(r-r¹)/ 4πε₀(r-r¹)³

Similarly for N charges , the electric field intensity at ‘r’ is given by ,

E =

Electric fields due to charge distributions:

Line charge:

Fig-1:

Consider a line charge with uniform charge density ‘ρ_L’ extending from A to B along the Z-axis . The charge dQ associated with dl = dz of the line is dQ = ρL.dl= ρL.dz

& hence total charge Q is Q =