Question

the value of mu 0/4pi =10^-7 in SI units. Find its value in CGS units,(mu 0 = permeability of free space)

Answer 1

Explanation:

The physical constant μ 0

commonly called the vacuum permeability, permeability of free space, ... In the reference medium of classical vacuum, μ0 has an exact defined value: .... The value of μ 0 was chosen such that the rmks unit of current is equal in size to the ampere in the emu system: μ0 is defined to be 4π×10-⁷ H/m.

Answer 2

The value of μ₀/4π in CGS units will be 10⁻¹⁴

• It is given to us that the value of μ₀/4π in SI units is equal to 10⁻⁷.
• We know that the units of the given value  μ₀/4π are equal to H/m (Henries per meter), which is further equivalent to NA⁻² (Kg.m.A⁻².s⁻²), newtons per ampere squared.
• Converting the SI unit of  μ₀/4π to CGS units, we obtain g.cm.Bi⁻².s⁻²
• The CGS equivalent of current is abampere (aBA or Bi).  
• 1 Bi = 10 A
• Unit conversion from SI to CGS can be carried out using dimensional analysis.
• According to dimensional analysis, the following formula will be used:

                                    n₂ = n₁ (M₁/M₂)ᵃ(L₁/L₂)ᵇ(T₁/T₂)ⁿ(A₁/A₂)ˣ

• The dimensional formula for  μ₀/4π is [MLT⁻²A⁻² ].

n₂ = 10⁻⁷(1/1000)¹(1/100)¹(1/1)⁻²(10/1)⁻²

n₂= 10⁻⁷⁻³⁻²⁻² = 10⁻¹⁴

Thus, the value of μ₀/4π in CGS units will be 10⁻¹⁴.