Dimensional formula of permittivity of free space

Permittivity of free space
[M−1 L−3 T4 A2]
Written in full: [M⁻¹ L⁻³ T⁴ A² K⁰]

How to derive it

Permittivity of free space = Charge² ÷ (4π × Force × Distance²), from Coulomb's law

Put in the dimensions of each part: [AT]² ÷ ([MLT⁻²] × [L²]) = [M⁻¹ L⁻³ T⁴ A²].

mass (M)
-1
length (L)
-3
time (T)
4
current (A)
2
temperature (K)
0

SI unit

The SI unit of permittivity of free space is C²/(N·m²).

Same dimensions as permittivity of free space

None of the other quantities on this site share these exact dimensions.

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More from Electrostatics

QuantityFormula
Electric charge[T A]
Electric potential[M L2 T−3 A−1]
Electric field[M L T−3 A−1]
Electric flux[M L3 T−3 A−1]
Electric dipole moment[L T A]
Capacitance[M−1 L−2 T4 A2]