Electric Power Generation, Transmission, and Distribution

The horizontal and vertical components of the electric field are

Ei_x¼

Qi

2 p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðÞxiX^2 þðÞyiY^2

q sin (Fi)¼

Qi

2 p

xiX

ðÞxiX^2 þðÞyiY^2



Ei_y¼

Qi

2 p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðÞxiX^2 þðÞyiY^2

q cos (Fi)¼

Qi

2 p

yiY

ðÞxiX^2 þðÞyiY^2



Thexandycomponents generated by all six charges are calculated using the equations above.
The magnitude of the total electric field is calculated by the summation of the components. The
magnitude of the total field is

E¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

X

i

Ei_x

! 2

þ

X

i

Ei_y

vu! 2

ut

For the demonstration of the expected results, we calculated a 500-kV transmission line generated
electric field magnitude under the line in 1 m distance from the ground. The conductors are arranged
horizontally. The average conductor height is 24.38 m (80 ft); the distance between the conductors is
10.66 m (35 ft). The line-to-ground voltage is

Vln¼

500 kV

ffiffiffi

3

p ¼ 288 :7kV

Conductor

(xi, yi)

Electrical Field

Line

Q

Ground

Ex

E Ey

r

(xi − X)

(y

−i

Y

)

Φ

Point of Observation

(X, Y)

Φ

FIGURE 19.10 Electric field generated by a charge in an observation point (X,Y).