493
of water [Equation 5.11 on page 150];ρ(1md)linear mass density (mass per length)
[Your Turn 12b on page 454]
ρqbulk charge density (charge per unit volume) [Equation 7.20 on page 232];ρq,macro,
charge density of impermeant macromolecules in a cell [Equation 11.3 on page 414]
Σsurface tension [Section 7.2.1 on page 219]
σsurface density (things per unit area) [Section 1.4.4 on page 19];σqsurface density of
electric charge [Equation 7.27 on page 236]
σchanarea density of ion channels in a membrane [Problem 12.9 on page 485]
σwidth of a Gaussian distribution; standard deviation of any probability distribution;
σ^2 ,variance of a distribution [Section 3.1.3 on page 69]
τtorque
τtime constant for some relaxation process [Equation 6.30 on page 196]; time constant
for electrotonus [Equation 12.8 on page 452]
φvolume fraction, dimensionless [Section 7.2.1 on page 219]
Ψgrand potential [Problem 8.8]
Ωnumber of available states [Section 6.2.2 on page 177]
ωtwist density (torsional deformation) of a polymer [Section 9.1.2 on page 302]Dimensions
Most physical quantities carry dimensions. In this book we refer to abstract dimensions by the
symbolsL(length),T(time),M(mass), andQ(charge). (The abstract dimension for temperature
has no symbol in this book.)
Some quantities are dimensionless, for example geometrical angles: The angle of a pie wedge
equals the circumference divided by the radius, so the dimensions cancel.
Units
There shall be standard measures of wine, beer, and corn
throughout the whole of our kingdom...and there shall be stan-
dard weights also. – Magna Carta, 1215
This book primarily uses the Syst`eme Internationale of units; but, when appropriate, convenient,
or traditional, some outside units are also used.
SI Base Units Corresponding to the abstract dimensions listed above, we use five of the seven
SI base units:
1.Length - The meter (m)has dimensionsL.Itisdefined as the length of the path travelled by
light in vacuum during a time interval (1/299 792 458)s.
2.Time - The second (s)has dimensionsT.Itisdefined as the duration of 9 192 631 770 periods
of the radiation corresponding to the transition between the two hyperfine levels of the ground
state of the cesium-133 atom.
3.Mass - The kilogram (kg)has dimensionsM.Itisdefined as the mass of a particular object,
called the international prototype of the kilogram.
4.Electric Current - The ampere (A)has dimensionsQT−^1 .Itisdefined as the constant current
which, if maintained in two straight parallel wires of infinite length placed 1 meter apart in