Dimensional formula of Permittivity of free space

How to get the dimensional formula of permittivity of free space

1. Start from the definition: permittivity of free space = electric charge² / (force × length²).
2. electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
3. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
4. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
5. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
6. Put in the dimension of each part: [T A]² / ([M L T^-2] × [L]²).
7. Add the powers of each base quantity: [M^-1 L^-3 T⁴ A²].

Three questions on permittivity of free space

Related quantities

• G Gravitational constant [M⁻¹ L³ T⁻²]
• c Speed of light [L T⁻¹]
• h Planck's constant [M L² T⁻¹]
• ħ Reduced Planck's constant (h-bar) [M L² T⁻¹]
• k Boltzmann constant [M L² T⁻² K⁻¹]
• R Universal gas constant [M L² T⁻² K⁻¹ mol⁻¹]