Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

14 CHAPTER 2
(C), is defined in terms of electric current rather than by Coulomb’s law. For this
reason, the constant of proportionality has a value not equal to 1 but rather
9 N · m2
k0 = 9 × 10
C 2
(2.25)
when the two charges are in a vacuum or in air (air at atmospheric pressure exerts very
little influence on the force developed between charges and thus may be considered
equivalent to a vacuum). The subscript 0 signifies the value of k in a vacuum. If
the charges are separated by materials, other than air, that are poor conductors of
electricity (such materials are called dielectrics), the value of k is different and depends
on the material.
It is convenient to define k0 in terms of another constant, ε0, called the permittivity:
k0 = 1
= 9 × 10
4πε0
ε0 = 1
=
4πk0
9 N · m2
, (2.26)
C 2
1
N · m2
4π × 9 × 109 C 2
= 8.85 × 10 −12
C2 ,
N · m2 where ε0 is the permittivity of a vacuum. The permittivity of any other medium is
designated by ε. The relative permittivity, Ke , of a substance is defined by
Ke = ε
(2.27)
ε0
and is called the dielectric coefficient.
For all dielectric materials, the dielectric coefficient has a value greater than 1.
The permittivity, or the dielectric coefficient, is a measure of the amount of electric
energy that can be stored in a medium when the medium is placed into a given
electric field. If everything else is held constant, a higher dielectric coefficient leads
to a greater amount of stored electric energy.
The smallest natural quantity of electric charge is the charge on the electron or
proton, ±1.6 × 10 −19 C. The reciprocal of the electronic charge, 6.25 × 10 18 , is the
number of electrons whose aggregate charge is 1 C. In the cgs system, the unit of
charge is the statcoulomb (sC) and the electronic charge is 4.8 × 10 −10 sC. There are
3 × 10 9 sC in 1 C.
W EXAMPLE 2.4
Compare the electrical and gravitational forces of attraction between an electron
and a proton separated by 5 × 10 −11 m.
Solution
The electrical force is given by Eq. (2.24):
q1q2
N · m2
f = k0 = 9 × 109
r 2 C2 × 1.6 × 10−19 C × 1.6 × 10 −19 C
5 × 10−11 2
m
= 9.2 × 10 −8 N.