# 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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