Page 21 - Fiber Optic Communications Fund

2 Fiber Optic Communications

F 2
q 2

r

q 1
r

Figure 1.1 Force of attraction or repulsion between charges.

The electric field intensity is defined as the force on a positive unit charge and is given by Eq. (1.4). The
electric field intensity is a function only of the charge q and the distance between the test charge and q .
1
1
For historical reasons, the product of electric field intensity and permittivity is defined as the electric flux
density D,
q 1
D = E = r. (1.5)
4r 2
The electric flux density is a vector with its direction the same as the electric field intensity. Imagine a sphere
S of radius r around the charge q as shown in Fig. 1.2. Consider an incremental area ΔS on the sphere. The
1
electric flux crossing this surface is defined as the product of the normal component of D and the area ΔS.
Flux crossing ΔS =Δ = D ΔS, (1.6)
n
where D is the normal component of D. The direction of the electric flux density is normal to the surface of
n
2
the sphere and therefore, from Eq. (1.5), we obtain D = q ∕4r . If we add the differential contributions to
n
1
the flux from all the incremental surfaces of the sphere, we obtain the total electric flux passing through the
sphere,
= d = D dS. (1.7)
∫ ∮ n
S
D

D
q 1

s
Δs
(a) (b)

Figure 1.2 (a) Electric flux density on the surface of the sphere. (b) The incremental surface ΔS on the sphere.