1Which is the dimensional formula of Coulomb constant?
Coulomb constant works out to [M L³ T⁻⁴ A⁻²].
Fundamental constantsClass 12, Electric Charges and Fields
Dimensional formula of Coulomb constant
[M L3 T-4 A-2]
The k = 1/(4πε0) in Coulomb's law, about 9 × 10⁹ N m²/C².
How to get the dimensional formula of Coulomb constant
- Start from the definition: Coulomb constant = force × length2 / electric charge2.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
- Put in the dimension of each part: [M L T-2] × [L]2 / [T A]2.
- Add the powers of each base quantity: [M L3 T-4 A-2].
Three questions on Coulomb constant
2What is the SI unit of Coulomb constant?
The SI unit of Coulomb constant is the newton metre squared per coulomb squared (N m²/C²).
3Do Coulomb constant and permeability of free space have the same dimensions?
Coulomb constant is [M L³ T⁻⁴ A⁻²] but permeability of free space is [M L T⁻² A⁻²].
Coulomb constant: quick answers
What is the dimensional formula of Coulomb constant?
The dimensional formula of Coulomb constant is [M L³ T⁻⁴ A⁻²]. It comes from Coulomb constant = force × length² / electric charge².
What is the SI unit of Coulomb constant?
The SI unit of Coulomb constant is the newton metre squared per coulomb squared (N m²/C²).
Is Coulomb constant dimensionless?
No. Coulomb constant has the dimensions [M L³ T⁻⁴ A⁻²].