Check the dimensional correctness of c = 1/√(μ₀ε₀)
Speed of light from μ₀ and ε₀. Maxwell's result that links light to electricity and magnetism.
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
c = 1 / sqrt(μ0 ε0)c[L T-1]=1/sqrt(mu0 epsilon0)[L T-1]Step by step
1. What each symbol stands for
- c speed of light [L T-1]
- μ0 permeability of free space [M L T-2 A-2]
- ε0 permittivity of free space [M-1 L-3 T4 A2]
2. The dimensions of each term
- c [L T-1] [L T-1]
- 1/sqrt(mu0 epsilon0) 1 / sqrt([M L T-2 A-2] × [M-1 L-3 T4 A2]) [L T-1]
3. Compare
Every term has dimensions [L T-1], so the equation is dimensionally consistent.
What it proves and what it does not
It can show
- Every term that is added or subtracted has the same dimensions, so the sum makes sense.
- Both sides of the equals sign have the same dimensions.
- Angles inside sin, cos and similar functions are pure numbers.
It cannot show
- A pure number such as 1/2 or 2π has no dimensions, so a check cannot see a missing or wrong one.
- Two quantities with the same dimensions, such as work and torque, cannot be told apart.
- A sign error or a wrong power that keeps the dimensions equal goes unnoticed.
Matching dimensions are necessary but not sufficient. Pure numbers such as 1/2 or 2π have no dimensions, so a check cannot see them, and an equation with matching dimensions can still be wrong.
Look up each quantity
c = 1/√(μ₀ε₀): quick answers
Is c = 1/√(μ₀ε₀) dimensionally correct?
Yes. Every term has the same dimensions, [L T⁻¹], so c = 1/√(μ₀ε₀) is dimensionally consistent. That does not prove the equation itself is correct.
Does a dimension check prove c = 1/√(μ₀ε₀) is right?
No. A check can show that an equation is wrong, but it cannot show that it is right. Pure numbers such as 1/2 and 2π have no dimensions, so the check cannot see them.