The dimensional formula of a Tesla (T), the SI unit of magnetic flux density, is [M T-2 I-1], where M represents mass, T represents time, and I represents electric current.
Understanding the Dimensional Formula
A Tesla is defined as one Weber per square meter (1 T = 1 Wb/m²). The dimensional analysis helps break down this unit into its fundamental components.
- Magnetic Flux (Weber, Wb): The Weber can be expressed in terms of other SI units as V⋅s (Volt-seconds).
- Volt (V): A volt can be defined in terms of energy (joules) per unit charge (coulombs): V = J/C. Joule is the SI unit of Energy and Coulomb is the SI unit of electric charge.
- Joule (J): The joule is the SI unit of energy, and its dimensions are [M L2 T-2] (mass × (length)2 × (time)-2).
- Coulomb (C): The coulomb is the SI unit of electric charge, and it can be expressed as I⋅T (current × time).
Therefore, we can express Tesla (T) in terms of the fundamental units:
- Weber (Wb): Since 1 Wb = 1 V⋅s, and V = J/C, then Wb = (J/C) s = (M L2 T-2 / I T) T = [M L2 T-1 I-1]
- Tesla (T = Wb/m2): T = [M L2 T-1 I-1] / [L2] = [M T-2 I-1]
Breakdown of the Dimensions
- M: Mass
- T-2: Inverse square of Time
- I-1: Inverse of Electric Current
Significance
Understanding the dimensional formula is crucial for:
- Verifying the correctness of equations: Ensuring that the dimensions on both sides of an equation match.
- Converting units: Facilitating the conversion between different units within the same system.
- Deriving new relationships: Helping to identify potential relationships between physical quantities.
