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Re: How many joules --> e.m. waves?



LUDWIK KOWALSKI wrote:

EURECA

The radiation resistance of our antenna, which is an oscillating magnetic
dipole, can be calculated from the following formula. The derivation is
not trivial (I skipped it) but the formula is simple.

R_rad = (4*PI/3)*sqrt(mu/epsilon)*(2*PI*A/lmd)^4 = 2.46e6*(A/lmd)^4

where A is the area of the loop and lmd is the wavelength. For C=30 pF
and L=0.083 mH we have f=3.19e6 Hz and lmb=c/f=94 meters. The area of
our antenna (r=9 m) is 28.3 m^2 and R_rad=20100 ohms.
. . .
Just before posting I noticed something I do not like in the formula.
The last factor is not dimensionless unless A a length rather than the
area. I suspect a typographical error (however, A was clearly defined
on the previous page as Pi*r^2). The dimensional analysis (see below)
shows that R_rad is not in ohms when A is an area. Can somebody verify
the formula for R_rad of a magnetic dipole?
. . .

Ludwik Kowalski

Ludwig,
I find the following for the radiation resistance of the loop magnetic
dipole
(in Classical Electromagnetic Radiation, 3rd ed. 1995, Heald & Marion,
pg 331):

R = [(PI^5)/6]*Sqrt(mu/epsilon)*(d/lmb)^4 =19200*(d/lmb)^4 ohms, where d
= loop diameter.

Inputing your figures, R = 19200*(18/94)^4 = 25.8 ohms.
--
Bob Sciamanda sciamanda@edinboro.edu
Dept of Physics sciamanda@worldnet.att.net
Edinboro Univ of PA http://www.edinboro.edu/~sciamanda/home.html
Edinboro, PA (814)838-7185