CHAP. 12: BASIC TERMS OF CHEMICAL PHYSICS [CONTENTS] 413
whereQis the electric charge given in coulombs,~ris the vector determining the position of
the point in relation to the charge, andεis thepermittivityof the surrounding environment.
The lowest value of permittivity is that of vacuum,ε 0 = 8. 854 × 10 −^12 C^2 N−^1 m−^2. Other
environments exhibit a higher permittivity, which is usually expressed using therelative per-
mittivity
εr=ε
ε 0. (12.2)
Relative permittivity shows the ability of a substance to weaken the electric field, and it may
be determined by measuring the ratio between the capacitanceCof a capacitor with the given
substance and another with vacuum,C 0 ,εr=C
C 0
.
Note:In older literature, relative permittivity is called the dielectric constant.U Main units:permittivity: C^2 N−^1 m−^2 , relative permittivity is a dimensionless number.
Example
Determine the relative permittivity of water if you know that the capacitance of a capacitor with
an empty cell is 5 pF, and that it increases to 390 pF after the cell is filled with water. Assume
that the capacitance is determined solely by the filling of the cell.Solution
The capacitance of the capacitor is proportional to the permittivity of the space between the
electrodes. With the cell empty, the permittivity is very close to that of vacuum. The relative
permittivity of water is thus equal to the ratio between both capacitances,εr=C
C 0
=
390 pF
5 pF