Derive the unit of speed from the product of the permittivityand permeability of

Question

Derive the unit of speed from the product of the permittivityand permeability of free space, starting from their originalunits. I started it as c=00, then substituted for variables:m/s=(C2/Nm2)(Tm/A). Is there a way to furthersubstitute and cancel variables to get the right hand side of theequation to simplify to m/s? Derive the unit of speed from the product of the permittivityand permeability of free space, starting from their originalunits. I started it as c=00, then substituted for variables:m/s=(C2/Nm2)(Tm/A). Is there a way to furthersubstitute and cancel variables to get the right hand side of theequation to simplify to m/s?

Explanation / Answer

Remember that some units can be written in terms of others: 1 Ampere is 1 Coulomb per second, so C = As 1 Newton is 1 meter-kilogram per second squared, so N = m kgs-2 1 Tesla is 1 kilogram per Ampere-(second squared), so T = kgA-1 s-2 Unit of the vacuum permittivity, o in SI baseunits: A2 s4 kg-1 m-3,where A is Amperes, s is second, kg is kilograms and m ismeters. Unit of the vacuum permeability, o in SI baseunits: m kg s-2 A-2. So the units of oo isA2 s4 kg-1 m-3(m kgs-2 A-2) = m-2s2, whichis the inverse squared of the units of speed. Since c2 = 1/(oo),this is correct.

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