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

V
a
b
REVIEW OF PHYSICAL PRINCIPLES 25
The electric intensity throughout the region between the two plates is ε newtons
per coulomb. The force acting on any charge within this field therefore is
f = εq N. (2.36)
If the charge q happens to be positive, then to move it across the distance d, from
the negative to the positive plates, against the electric force in the uniform field
requires the expenditure of energy given by the equation
W = fd = εqd. (2.37)
However, since potential difference (V ) is defined as work per unit charge,
Eq. (2.37) may be expressed as
or
V = W
q
ε = V
d
= εd, (2.38)
V
. (2.39)
m
Equation (2.39) expresses electric field intensity in the units most commonly used
for this purpose—volts per meter.
A nonuniform electric field that is of interest to the health physicist (in instrument
design) is that due to a potential difference applied across two coaxial conductors,
as shown in Figure 2-7. If the radius of the inner conductor is a meters and that of
the outer conductor is b meters, then the electric intensity at any point between the
two conductors, r meters from the center, is given by
ε = 1
r ×
ln
V
b
a
V
, (2.40)
m
where V is the potential difference between the two conductors.
r
Figure 2-7. Conditions for the nonuniform
electric field between two coaxial
conductors given by Eq. (2.40).