During the kite experiment, Benjamin Franklin put an iron stalk on the kite. As he wanted to prove the similarities between lightning and electricity, that was an exellent reasoning.
Indeed, a law regarding electricity was discovered after Franklin’s life-time. It tells us the smaller an object is, the stronger its electric field is near it. The law involved is Gauss’ law.
Where E is the value of the electric field in a point near the sphere,
1/(4πε) is a constant ( also called k),
Q the total electric charge of the sphere,
and r the radius from the source to the point.
E(S1)= k*Q*(1/R²)= (k*Q)/(2r)²= (k*Q)/r² * ¼
= ¼ E(S2)
E(S2)= k*Q*(1/r²)= (k*Q)/r²= (k*Q)/r²= 4 E(S1)
E is inversely proportional to r squared
That proves that with a radius twice smaller, S2 owns an electric field 4 times stronger near it.
If we apply that principle to an infinitely small object, its electric field will be infinitely strong near it. And if we identify a point as a small object, its electric field is strongly worth. It is an important factor that allows the ionization of the air particles wich determines the path of the lightning.