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Electromagnetic field strength

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roboticmehdi
#1
Mar19-12, 07:32 AM
P: 34
hello world. it is know that electrostatic (coulomb's law) and magnetostatic (biot-savart law) fields lose their strength like 1/r^2. why do they say that electromagnetic field falls like 1/r ? is that true ? if yes how, can you explain please ? after all energy radiated from a point source must fall like 1/r^2, because the area of surface of a sphere increases like r^2.
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DaleSpam
#2
Mar19-12, 07:42 AM
Mentor
P: 16,942
Quote Quote by roboticmehdi View Post
why do they say that electromagnetic field falls like 1/r ?
Can you provide a reference for this? It is hard to say one way or the other without knowing the details.
roboticmehdi
#3
Mar19-12, 07:48 AM
P: 34
Quote Quote by DaleSpam View Post
Can you provide a reference for this? It is hard to say one way or the other without knowing the details.
http://en.wikipedia.org/wiki/Larmor_formula there in the part ''Derivation 2: Using Edward M. Purcell approach'' it says stuff related to this.

DaleSpam
#4
Mar19-12, 08:03 AM
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P: 16,942
Electromagnetic field strength

Both Coulomb's law and the Biot-Savart law are approximations for 0 velocity and 0 acceleration respectively. The full general field produced by a point charge moving with arbitrary velocity and acceleration is given by the Lienard Wiechert potential:
http://en.wikipedia.org/wiki/Li%C3%A...hert_potential

If you look at the formula for the LW fields you see that for a stationary charge you get a 0 B field and a 1/r E field, corresponding with Coulomb's law. If you look at the formula for the LW fields for a moving but not accelerating charge you get a 1/r B field, corresponding with the Biot-Savart law. However, if you look at the formula for an accelerating charge you also get a 1/r E and a 1/r B field.
Philip Wood
#5
Mar20-12, 04:46 AM
PF Gold
P: 936
One way to shed light on this is to note that the 1/r fields (unlike the 1/r2 fields) are propagating away from the source, carrying energy with them. In a wave, the intensity (energy per unit time per unit normal area) is proportional to the square of the amplitude, so to 1/r2 for the 1/r propagating field. But this 1/r2 intensity law is just what we get by assuming energy not to be lost from the wave as it propagates outwards through larger and larger spherical surfaces whose areas are proportional to r2.


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