# Re: [TCML] Spark dynamics on Jacobs Ladder

```Hi Bert,

```
...thanks for the very lucid demonstration and formulas of the relative merits of the magnetic and electric field, regarding mechanical force. I "think" many of us "electric-people" are used to think "current flow" by habit, when noticing "force", instead of considering electrostatic attraction as well (myself included; may be, 'cause of the many motors around).
```
```
When doing the experiments of "Jacobsladder-Oscillator", I also made some calculations, which show the relative merits of electric vs. magnetic forces in this case:
```
http://www.pupman.com/listarchives/2007/Mar/msg00673.html

Best regards

Kurt

Bert Hickman wrote:
```
```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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