A physical quantity of the dimensions of length that can be formed out of c, G and (e²)/(4πε₀) is, where c is the velocity of light, G is the universal constant of gravitation and e is charge:

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(4) 1/(c²)[G(e²)/(4πε₀)]^1/2. Idea: build the dimensional formula of each ingredient first. [(e²)/(4πε₀)] is an energy times a length: [ML³T⁻²] [G]=[M⁻¹L³T⁻²] [G(e²)/(4πε₀)]=[M⁻¹L³T⁻²][ML³T⁻²]=[L⁶T⁻⁴] Taking the square root: [L³T⁻²] [c²]=[L²T⁻²], so dividing removes the time: ([L³T⁻²])/([L²T⁻²])=[L]

A physical quantity of the dimensions of length that can be formed out of c, G and (e²)/(4πε₀) is, where c is the velocity of light, G is the universal constant of gravitation and e is charge:

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