Chapter 2: E-field of Two Line Charges Having Same Polarity & Opposite Polarity

Illustration 2

Electric Field Distribution in the Cross-Section of Infinitely Long Transmission Lines

Ø      Parallel-plate line

Ø      Coaxial line

Ø      Two-wire line

 

 

 

 

 



Parallel-plate Line

The parallel-plate line consists of two parallel metallic plates in close proximity. Often between the plates a dielectric layer is placed. Here, however, we assume that the medium between the plates is simply air. Figure 1 is a map of the E-field where the arrows show the direction of the vector and their color represents its intensity. Figure 2 plots the magnitude of the E-field along a vertical line intersecting the plates right in the middle.

Notice that: (1) the field is practically constant almost everywhere between the plates; (2) at the edge of each plate, the field stream lines curve and even “leak out” in the surrounding medium (edge effect); (3) the field is weak but not zero outside of the volume sandwiched between the plates as the structure is open; the closer the two plates to each other, the less the leakage (4) at the corners of the metallic plates, the field magnitude is extremely high (field singularity).

 
Figures (click to enlarge)
Figure 1

Figure 2

 

Figure 1

Figure 2

 



Coaxial Line

The coaxial line consists of two concentric conductors: the inner wire is typically a monolithic conductor, while the outer conductor, called the shield, is often made of many thin wires. Often the medium between the plates has dielectric properties. Here, however, we assume that the medium is simply air. Figure 1 is a map of the E-field where the arrows show the direction of the vector and their color represents its intensity. Figure 2 plots the magnitude of the E-field along a radial line from the center of the inner wire to the outer edge of the shield.

Notice that: (1) only one quarter of the cross-section is given since the structure is circularly symmetrical; (2) the field decreases as  where  is the radial distance; (3) there is no field “leakage” outside the line since the structure is fully electrically closed (shielded).

 
Figures (click to enlarge)
Figure 1

Figure 2

 

 

Figure 1

Figure 2

 



Two-wire Line

The two-wire line consists of two parallel cylindrical conductors in close proximity. Typically, the two wires have potentials of the same magnitude but opposite signs. The medium between the wires is air. Figure 1 is a map of the E-field where the arrows show the direction of the vector and their color represents its intensity. Figure 2 plots the magnitude of the E-field along the line connecting the centers of the two wires.

Notice that the field is quite strong even far from the wires because the structure is completely open.

 
Figures (click to enlarge)
Figure 1

Figure 2

 

 

Figure 1

Figure 2