Final answer:
To verify the speed of light using the permeability and permittivity of free space, the equation c = √(μ0ε0) is used. Substituting the known values of μ0 and ε0 into this equation should yield the established value of approximately 2.998 x 10^8 m/s.
Step-by-step explanation:
To verify that the correct value for the speed of light (c) is obtained, we use the equation c = √(μ0ε0), where μ0 represents the permeability of free space and ε0 represents the permittivity of free space. The values given for these constants in the International System of Units (SI) are μ0 = 4π x 10^-7 N/A^2 (newton per ampere squared) and ε0 = 8.854187817 x 10^-12 C^2/N⋅m^2 (coulombs squared per newton per meter squared). When we substitute these values into the equation and calculate, the result should be approximately c = 2.998 x 10^8 m/s, which matches the established value of the speed of light in a vacuum.
The units for the equation derive from μ0 and ε0, which combine to give units of m^2/s^2. Taking the square root gives us units of m/s, which are the correct SI units for speed.