Question

The speed of light in vaccum (c), depends on two fundamental constants, the permeability of free space (μ₀) and permittivity of free space (ϵ₀). The speed of light is given by c =1/√μ₀ ϵ₀. The units of ϵ₀ are N⁻¹C²m⁻². The units for μ₀ are

a. kg⁻¹m⁻¹C²
b. kg m C⁻²
c. kg⁻¹mC²
d. kg⁻¹s⁻¹C²

Answer 1

The correct unit for the permeability of free space (μ₀) is option (b) kg m C⁻².

Step-by-step explanation:

The speed of light in a vacuum, denoted as c, is a fundamental constant in physics and is calculated using the permeability (μ₀) and permittivity of free space (ϵ₀) with the equation c = 1/√(μ₀ϵ₀). The unit for the permittivity of free space (ϵ₀) is given as Newtons per Coulomb squared meters squared (N⁻¹C²m⁻²). The correct unit for the permeability of free space (μ₀) is then derived from rearranging this equation and considering that speed (c) has units of meters per second (m/s). By performing dimensional analysis, we find that the correct unit for μ₀ is kilogram meter per second squared per Coulomb squared (kg m s⁻² C⁻²), which matches the option (b) kg m C⁻².