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376 ⏐⏐⏐ CAPACITORS
+ +
(a)
+ –
(b)
FIG. 10.2
Electric flux distribution: (a) like charges;
(b) opposite charges.
Electric
flux lines
The larger the charge Q in coulombs, the greater the number of flux
lines extending or terminating per unit area, independent of the surrounding
medium. Twice the charge will produce twice the flux per unit
area. The two can therefore be equated:
(coulombs, C) (10.2)
By definition, the electric field strength at a point is the force acting
on a unit positive charge at that point; that is,
F
� � �� Q
a
r2 r1 +
w � Q
(newtons/coulomb, N/C) (10.3)
The force exerted on a unit positive charge (Q2 � 1 C), by a charge
Q1, r meters away, as determined by Coulomb’s law is
F � � kQ1Q2
�2 � �
r
kQ1(1)
�2 � �
r
kQ1
� 2 (k � 9 � 10
r
9 N.m 2 /C 2 )
Substituting this force F into Eq. (10.3) yields
kQ1/r � � �
2
F
� �
Q2 1
� � � kQ1
�2
r
(N/C) (10.4)
We can therefore conclude that the electric field strength at any point
distance r from a point charge of Q coulombs is directly proportional to
the magnitude of the charge and inversely proportional to the distance
squared from the charge. The squared term in the denominator will
result in a rapid decrease in the strength of the electric field with distance
from the point charge. In Fig. 10.1, substituting distances r1 and
r2 into Eq. (10.4) will verify our previous conclusion that the electric
field strength is greater at a than at b.
Electric flux lines always extend from a positively charged body to a
negatively charged body, always extend or terminate perpendicular to
the charged surfaces, and never intersect.
For two charges of similar and opposite polarities, the flux distribution
would appear as shown in Fig. 10.2.
b
Positive charge
Flux lines radiate
outward for positive
charges and inward
for negative charges.
FIG. 10.1
Flux distribution from an isolated positive charge.