Dimensional formula of Relative permittivity

How to get the dimensional formula of relative permittivity

1. Start from the definition: relative permittivity = capacitance / capacitance.
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. energy = mass × velocity², so energy is [M] × [L T^-1]² = [M L² T^-2].
5. electric potential = energy / electric charge, so electric potential is [M L² T^-2] / [T A] = [M L² T^-3 A^-1].
6. capacitance = electric charge / electric potential, so capacitance is [T A] / [M L² T^-3 A^-1] = [M^-1 L^-2 T⁴ A²].
7. Put in the dimension of each part: [M^-1 L^-2 T⁴ A²] / [M^-1 L^-2 T⁴ A²].
8. Add the powers of each base quantity: [M⁰ L⁰ T⁰].

Quantities with the dimensions [M⁰ L⁰ T⁰]

• Angle
• Solid angle
• Coefficient of friction
• Coefficient of restitution
• Relative density
• Strain
• Poisson's ratio
• Reynolds number
• Emissivity
• Ratio of specific heats
• Sound level
• Magnetic susceptibility
• Relative permeability
• Power factor
• Quality factor
• Refractive index
• Magnification

Equal dimensions do not make them the same quantity. Compare relative permittivity with the others in the full grid.

Three questions on relative permittivity

Related quantities

• q Electric charge [T A]
• E Electric field [M L T⁻³ A⁻¹]
• V Electric potential [M L² T⁻³ A⁻¹]
• V Potential difference [M L² T⁻³ A⁻¹]
• ε Electromotive force (emf) [M L² T⁻³ A⁻¹]
• U_E Electric potential energy [M L² T⁻²]