Units and Dimensions of Charge and Permittivity
Covers the SI units (Coulomb for charge, Farad per meter for permittivity) and dimensional formulas for electric charge and permittivity of free space.
What is Units and Dimensions of Charge and Permittivity?
A fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. Measured in Coulombs (C).
Key formula / rule: Dimensional formula for Charge
Key points
- Identify the SI unit of electric charge.
- Determine the dimensional formula for electric charge.
- Identify the SI unit of permittivity of free space.
- Derive and state the dimensional formula for permittivity of free space.
Common exam trap
Confusing charge dimensions with current dimensions.
Definitions
- Term
Electric Charge
- Meaning
A fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. Measured in Coulombs (C).
- Term
Permittivity of Free Space (ε₀)
- Meaning
A physical constant representing the capability of a vacuum to permit electric lines of force. Its SI unit is Farad per meter (F/m).
- Term
Dimensional Formula
- Meaning
An expression that shows how the dimensions of a physical quantity relate to the fundamental dimensions (like mass, length, time, etc.).
Learning objectives
Identify the SI unit of electric charge.
Determine the dimensional formula for electric charge.
Identify the SI unit of permittivity of free space.
Derive and state the dimensional formula for permittivity of free space.
Apply dimensional analysis to electrostatic formulas.
Formulae
- Name
Dimensional formula for Charge
- Note
A = Ampere (Electric Current), T = Second (Time)
- Expression
[Q] = [A][T]
- Name
Dimensional formula for Permittivity of Free Space
- Note
M = Mass, L = Length, T = Time, A = Ampere
- Expression
[ε₀] = [M]⁻¹[L]⁻³[T]⁰[A]²
- Name
Coulomb's Law (for derivation)
- Note
Used to derive dimensions of ε₀
- Expression
F = ¹/⁴πε₀ * (q1*q2)/r²
Prerequisites
Basic understanding of SI units.
Knowledge of fundamental physical quantities and their dimensions (mass, length, time, current).
Familiarity with Coulomb's Law.
Common mistakes
Confusing charge dimensions with current dimensions.
Incorrectly deriving or remembering the dimensions of permittivity.
Using base SI units for charge instead of derived dimensions in dimensional analysis.
Keywords
Electric Charge
Coulomb
Permittivity of Free Space
Farad per meter
Dimensions
Dimensional Formula
SI Units
Coulomb's Law
Electrostatics
Practice preview
The dimensional formula for electric charge is:…
easy
Which of the following is the correct dimensional formula for the permittivity of free space (ε₀)?…
medium
The unit of electric charge is Coulomb. Which of the following statements about Coulomb is correct?…
medium