Dimensional Analysis: Deduce Dimension of Entropy, Surface Charge Density, etc.

[dan4loriel]

Homework Statement

how do i deduce the dimension of the following using dimensional analysis

enthropy, surface charge density, inductance, permitivity, radius of gyration

Homework Equations

The Attempt at a Solution

tried deducing the dimension of power like this:

p=work done/time
work done w= force x distance
=MLT e^-2 L
=ML e^T e^-2

substitute for power P= ML e^2 T e^ -2/T = ML e^ 2 T e^ -2

=ML e^ 2 T e^ -3

 

[jbsteele]

=MLT^-1 e^2 the dimension of power is MLT-1 Entropy: S = k log WK = Boltzman's constant and W = number of microstatesS = k log W =klog (M^N)=k (N log M)=kNT^0 The dimension of entropy is kNT^0Surface charge density: σ = q/Aq=charge and A= Areaσ = q/A = (MLT e^-2)/(ML^2) =M-1 T e^-2 L^-2 The dimension of surface charge density is M-1 T e^-2 L^-2 Inductance: L = μ0 N2 A/l μ0 = permeability and N=number of turns in coil, A=area of cross section, l = length of coil L = μ0 N2 A/l = (M T e^-2 L^-2) (MT^0)^2 (ML^2)/L =ML^2 T e^-2 L^-2 The dimension of inductance is ML^2 T e^-2 L^-2 Permitivity: εr = ε0 εr ε0= permittivity, εr= relative permittivity εr = ε0 εr = (M T e^-2 L^-3) (MT^0) =M T e^-2 L^-3 The dimension of permitivity is M T e^-2 L^-3 Radius of Gyration: k^2 = I/m I= moment of inertia, m= mass k^2 = I/m = (ML^2 T^-2) /(M) =L^2 T^-2 The dimension of radius of gyration is L^2 T^-2