# Re: RF biological hazards? (fwd)

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---------- Forwarded message ----------
Date: Tue, 5 May 1998 11:56:17 -0700
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: RF biological hazards? (fwd)

Here is a quick calculation of expected electric and magnetic fields,
assuming the tesla coil is a "short" dipole (that is, it is much shorter
than a wavelength). I calculated based on a total coil height of 1 meter,
with the secondary C of 40 pF and secondary L of 63 mH, for a resonant
frequency of 100 kHz. Further, I assumed the max secondary voltage was 1
megavolt. The calculated impedance of the coil is about 40K ohms (=
sqrt(L/C))

The maximum values for the "near" field of a short dipole are:

Electric = Q0 * L / ( 2 *pi * epsilon * r^3)
Magnetic = I0 * L / (4 * pi * r^2)

where L is the dipole length, r is the distance (presumed >> L, which may
not be valid), Q0 is max stored charge, I0 is maximum current,
epsilon=8.85E-12 F/m

Calculating stored charge (Q0) = C * V = 40E-12 * 1E6 = 40E-6 coulombs
Calculating max current (I0) = V / Z = 1E6 / 40E3 = 25 Amps

At a distance of 3 meters (about 10 feet):
E field = 40E-6 * 1/(2 * pi * 8.85E-12 * 3^3) = 26 kV/meter
H field = 25 * 1 /(4 * pi * 3^2) = .22 A/m

To compare, the 1991 limits, at 100 kHz, are:
H= 300 A/m... The TC is way under the limit
E= 500 V/m..  The TC is way over at 50 times the limit

Now, the ANSI guidelines actually refer to average power. A TC is typically
pulsed at some rate (like 120 pps) with the actual pulses not lasting very
long (say 166 uSec for a 100 kHz coil and a Q of around 10 ), so the duty
cycle is 2 %, and the average power is just at the limit.  You tube
coilers, with 100% duty cycle, on the other hand....

Another way to look at it is to take the total input power and distribute
it over a sphere of the appropriate radius. For our 3 meter example, the
sphere would have an area of 4*pi*9 = 113 square meters. If the coil had an
input power of 1 kW, the average power density would be somewhere around 10
W/square meter or 1 mW/sq cm. The ANSI limit for 100 kHz is 100 mW/sq cm,
so even allowing for field concentrations and near field peculiarities,
etc. you are in the right ballpark.

I guess what this all means is that a medium power coil can produce EM
fields that are well in excess of the ANSI limit (but we all knew that from
the smell of ozone and the big sparks).  It also means that if you are
running higher powers, multiple kVA, and you stand close to it, you are
going to get hammered by the RF.

Whether the RF has a deleterious effect is another story. Most of the ANSI
limits are based on thermal effects, and keeping the thermal load below
0.4W/kg (compare with 11 W/kg for running or swimming).  There is an
interesting footnote in one of my references which says:

"There is also the problem of possible electric shock or startle effects
with exposure to the full ANSI level below about 50 MHz, upon touching
metallic objects with the feet being adequately insulated from ground."

And perhaps the subject might be startled by that 5 foot arc waving in the
air? The loud sound of the spark gap, etc. Want to calculate the
capacitance from your feet to the ground? What is that impedance at 100 kHz
anyway?

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