Question

The speed of light in vacuum is defined to be c=299,792,458 m/s= 1. μ₀ε₀ The permeability constant of vacuum is defined to be μ₀=4π×10−⁷N⋅s²/C² Use these definitions to calculate the value of ε₀, the permittivity of free space, to at least eight significant figures. (Enter your answer in C²L(N⋅m² ).) C²L(N⋅m²)

Answer 1

The permittivity of free space, ε0, can be calculated using the given values for the speed of light and the permeability of free space. After performing the necessary substitutions and computations, ε0 is found to be approximately 8.854187817 × 10^−12 C2/N·m2.

Step-by-step explanation:

To calculate the value of ε0, the permittivity of free space, we can use the relationship between the speed of light (ε), the permeability of free space (μ0), and the permittivity of free space (ε0) which is given by the equation c = √(μ0ε0). The speed of light in a vacuum c is precisely defined to be 299,792,458 m/s. The permeability constant of vacuum μ0 is defined as 4π × 10^−7N·s2/C2.

Using these definitions, we can solve for ε0 as follows:

1. Rearrange the equation for c to solve for ε0:
   ε0 = 1 / (μ0 c2)
2. Substitute the values for μ0 and c:
   ε0 = 1 / ((4π × 10^−7 N·s2/C2) (299,792,458 m/s)2)
3. Compute the value for ε0:

After performing the calculation, ε0 is found to be approximately 8.854187817 × 10^−12 C2/N·m2.

The units (C2N−1m−2) confirm that when SI units for μ0 and ε0 are entered into the equation, the units provided are m/s, consistent with the speed of light.