Consider two charges of magnitude ๐₁ and ๐₂ , assumed to be concentrated as point sources at a distance d from each other.
According to the second law of electrostatics, the force F between them may be expressed mathematically as:
F∝q1×qkmfafaie2
F∝1d2
or F∝q1q2d2
F=k⋅q1q2d2N
..................................(1)
where, N is Newton and k is a Constant depending on the nature of the medium between the charges.
The value of k has been found experimentally,
k=14ฯฯต0ฯตr
....................................(2)
where ,
ฯตr
ฯต0
ฯต0
ฯต0
ฯต0
๐แตฃ is the relative permittivity of the medium intervening the charges
๐₀ is the permittivity of the evacuated free space
The value of ๐₀ in rationalised M.K.S. unit is 8.854×10⁻¹² farads per meter.
When d is measured in meters, the constant 4๐ , the proportionality factor for the rationalised M.K.S. units.
Substituting the value of k from Eq. (2) in Eq. (1) we get,
F=q1q24ฯฯต0ฯตrd2N
where,
๐₁ and ๐₂ are measured in coulombs
d in meters
๐ in farad / meter
F in newtons
For air ๐แตฃ = 1
∴ F=q1q24ฯฯต0d2N
when
๐₁ = ๐₂ = 1 coulomb
d = 1 meter
๐₀ = 8.854×10⁻¹² farad / meter
F=1×14ฯ×8.854×10−12×12
F=8.997×109
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