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A Different Picture of Radiation

Weldon Vlasak, Consultant, Adaptive Enterprises, adaptent@alltel.net

IntroductionA major difference between radiating and non-radiating fields is that the level of a non-radiating field decreases with the third power of the radius (volume), while the level of aradiating field decreases with the first power. The analysis presented here providesevidence as to how and why this occurs. The conclusions are somewhat surprising. It hasbeen accepted as fact that waves cannot move faster than the speed of light. However, itis only the propagation of signals in the radial direction that is limited to the speed oflight. Tangential waves travel much faster. Electromagnetic waves are not seen to breakaway, but to vary with the high tangential velocity of the field, producing a compressionof the wave and a corresponding time delay with distance.

AnalysisThe radiation equations for a dipole antenna can be found in various reference texts,including an early text by R. Mesny [ 1], and in more recent reference texts [ 2]:

3

30 cos- (cos - sin )r

I E u r u

r

=

(1)

2 2

3

sin(cos sin - cos )

2

30 I E u r u r u

r

+ t =

(2)

( )2sin

sin cos4

I H u r u

r

=

(3)

where = length of dipole

= wavelength

f = frequency I = current in dipole = angle transverse to dipole axis = 2 f r = radial distance from center of the dipole = 2 / u = ( t - r )

Then substituting the values of , u, = c / f , = 2 f and vt = r

3

30 cos- cos ( ) - sin (t r

v I r r E t t

c c cr

=

(4)

2

3 2

30 sinsin 1 cost t t

v v I r r E t t c c cr c

= + +

(5)

2

sinsin ( ) cos ( )

4

= +

t v I r r H t t r c c c

(6)

The absolute value of the E -field level of equation (5) is plotted versus radius in Figures1(a) and (b).

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0

30

60

90

120

150

180

210

240

270

300

330

5

4

3

2

1

0

5

0

rn

rn

rn

rn

1n 2 n, 3 n, 4n,

0

30

60

90

120

150

180

210

240

270

300

330

5

4

3

2

1

0

5

0

rn

rn

rn

rn

rn

rn

rn

rn

1n 2 n, 3n, 4n, 5n, 6n, 7n, 8n,

Figure 3(a). Plot of the two vectors of Figure 3(b). Rotating vectors at greaterequation (7) versus radius distances produces nearly circular patterns

Figure 3(a) includes both sets of vectors of Equation (2). Note that these vectors addalong the vertical axis and subtract along the horizontal axis. Figure 3(b) shows that theshape of the vectors becomes nearly circular in the far field. The three-dimensional wavesare actually in the form of hyperboloids (of two sheets).

0.1 1 1010

5

0

5

1010

10

E t1n

E t2n

E t3n

100.1 r n rn, rn,0.04 0.02 0 0.02 0.04

0.004

0.002

0

0.002

0.004

0.005

0.005

E sin n

0.050.05 E cos n

Figure 4(a). A plot of the radiation equation as Figure 4(b).The orthogonala function of radius at three consecutive time components of the radiatingincrements. wave plotted against one another at

one instant of time.

The linear plots of Figure 4 illustrate smooth progressions through the transition region.

Comments and Observations1. The above plots portray a gradual process where the ratio of the tangential field levelto that of the radial field increases with distance, thus contradicting earlier assertions thatelectromagnetic waves break away from the dipole and form closed loops that travel

through free space with speed c [4].

2. The curve of Figure 1(a) has a rather sharp break in the curve near r = . However, thesignal component curves of Figure 1(b) depict a smooth and more gradual transition fromthe near field to the far field.

3. The principle of Huyghens [5] asserts that sharp signals are transmitted as sharpsignals, propagating in rays through space. For a ray whose angle is fixed,

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r t const

c = =

. (8)

Solving equation (9) for r and differentiating,dr

cdt

= (9)

for any given ray.

4. It has been argued that the propagation of waves through space occur by virtue of theelectric field creating an electromagnetic wave, which in turn creates a subsequentelectric wave [ 3], similar to the action of an oscillating L-C circuit. However, in the farfield, both the transverse electric wave and the electromagnetic wave peak at the sameinstant of time [equations (7) and (8)], whereas exactly the opposite occurs for an L-Ccircuit.

5. The (1 v2 / c2) term in equations (16), (17) and (18) appear in various mathematicalmodels of physics and engineering. The Irish physicist, G. F. Fitzgerald proposed thatobjects grew shorter in the direction of their absolute motion, due to the pressure of the

ether wind [4]2

0 21v

L Lc

= . (10)The Fitzgerald contraction was analyzed by the Dutch physicist, H.A. Lorentz, whodeduced that mass increases inversely with the Fitzgerald ratio. Einstein argued that timedecreases in proportion to the Fitzgerald ratio in his General Theory of Relativity. A newmodel of the hydrogen atom, analyzed as an electric circuit, showed that the forces actingupon the electron are proportional to (1 v2 / c2), and other substantiating evidence for theabove assertion of the bending of electromagnetic waves was also presented [ 5].

Concluding RemarksThe plots of the radiation equations show that rotating or lateral motions of an electricfield wave must bend with its tangential velocity. If the rotating waves didn t bend, thenthe transfer of information through space would be instantaneous. Topological analysisallows a visualization of electromagnetic waves in space that are not always obtainableby the methods of abstract mathematics. This can lead to a better comprehension of theprocess by which radiation occurs. In this case, the issue of the change in dimensionalityof a radiating wave becomes clear. There are new systems that are being designed at themolecular level, which are potentially important in the future of science. Such designsmay involve treating atoms as tiny electrical circuits. The radiating and non-radiatingfields surrounding equations atoms and molecules will consequently be of concern.

References 1. Mesny, R. Radio- Electricite Generale , (Etienne Chiron, Paris France, 1935)2. Reference Data for Radio Engineers , Fifth Edition (Howard W. Sams & Co., Inc., New

York, 1973) p. 25-13. Halliday, D., and Resnick, R., Physics for Students of Science and Engineering II , (John

Wiley & Sons, New York, 1960), pp. 688-6914. Azimov, I., Understanding Physics, Magnetism and Electricity , Vol. II, (Barnes & Noble

Books, New York, 1993), pp. 96-1105. Vlasak, W., Secrets of the Atom , (Adaptive enterprises, Nebraska, 1999), Chapter VIII