// The formula for sphere gaps can be used for small gaps if the 30000 is replaced by
// the value obtained in this way divided by the distance d, but the formula above is
// enough for R>>d.
//

function E = Vbreakdown(d,p,T)
        // p = pressure in Torr (mm Hg),
        // d = distance in cm,
        // T = Temperature in Kelvins
        // Vbreakdown in kV
    x = 293 * p * d / (760 * T);
    E = 24.22 * x + 6.08 * x.^0.5;
    return E;
endfunction
    
    
function Vbrk=SparkGap(d)    
              // d separation in cm
R=3/4*2.54;   // ball radius cm
E=30;         // kV/cm break down voltage
    Vbrk = E*4000*d/(d/R+1+sqrt((d/R+1)^2+8))
    return Vbrk
endfunction

d=0.02:0.02:2;  // only a list of d separation values in cm
E=Vbreakdown(d,760,273+25);  // respective values in kV
plot(d,E./d)
set(gca(),"grid",[1 1]); // draw a grid in both axes
xtitle('Breakdown electric field ~Vs~ separation d','d  [cm]','E/d  [kV/cm]');