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Re: [TCML] Spark dynamics on Jacobs Ladder
Hi all,
I just took a look at the theoretical magnetic and electrical forces
between a pair of parallel conductors (simpler than diverging wires in a
JL, but should be close enough). Suppose we have a pair of parallel
wires in air with radius "a", separated by a distance "b" (where b>>a).
The magnetic and electrostatic forces per unit length (in Newtons/meter)
can be shown to be:
F(magnetic) = Fm = Uo*I^2/(2*Pi*b)
F(electrostatic) = Fe = Pi*€o*V^2/(2*b*(ln(b/a)^2))
where:
Uo = 4*pi*E-7 H/m
€o = 8.85*E-12 F/m
I = current flowing through both wires
V = voltage between wires
Now, suppose we plug in 0.25" diameter wires separated by 1.5", I =
0.030A, and V = 15,000 volts and solve for the respective electrostatic
and electromagnetic forces per meter of electrode length:
Fe = 1.33E-2 Newtons/meter
Fm = 4.72E-9 Newtons/meter
Thus, for Gary's NST-powered JL, the attractive $electrostatic force
between the wires (i.e., when the arc is not present) is about _three
million times greater_ than the repulsive magnetic force when the arc is
bridging the gap. This appears to provide theoretical support for the
experimental results described by Kurt Schraner.
If we increased the arc current to 50 amperes, then the magnetic force
becomes approximately equal to the electrostatic force at 15 kV for the
above wire geometry. If we increased the current to 50,000 amperes, the
magnetic force increases to 1.31E+4 Newtons/meter, or about 1 million
times greater than the electrostatic force. Since this force also acts
upon the arc itself, the arc is rapidly pushed away from the source of
power, as seen in the circular Jacobs Ladder and during some power line
arcs. This phenomenon is also used to sweep high current arcs across
electrodes (to reduce electrode evaporation in ultrahigh current closing
switches), and within certain vacuum power interrupters.
Reference: "Electric and Magnetic Forces Between Parallel-wire
Conductors", N. Morton, Physics Education, v14 n6 p369-73 Sept 1979.
Bert
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