Re: IONS/forces

[Ludwik Kowalski <kowalskiL@Mail.Montclair.edu>]

Bob Sciamanda wrote:

> Ludwik
> Are you sure that this isn't sqr(2)*R; (not 2*R)?  Or do
> I misread you? ....

If the distance were sqr(2)*R instead of 2*R, the pressure
would be 41% higher than 23.56 atmospheres (for Q=0.01 mC,
R=1 cm and a small opening in the shell). My first reaction
was to look for an error in the opposite direction, by orders
of magnitudes; because p was surprisingly large for only
10 micro-coulombs.

The discrepancy is probably connected with the opening
needed to avoid a singularity (at d=R where F must be
calculated). My ring-by-ring integration begins at the rim
of  the opening and covers the entire Q-dQ charge. The size
of the small opening has a negligible effect, as shown below.

The force at d=R (on the removed dQ, now treated as a
point-like probe charge) was calculated first. Then it was
divided by the area of the rim circle. For a very small
opening the calculated ratio is identified as pressure.

opening half-angle     pressure    each ring
       (degr)                        (atm)         (degr)

         10                           20.6237          10
          1                            23.2597            1
       0.1                            23.3360          0.1
     0.01                            23.5638         0.01
   0.001                            23.5666        0.001

       Ludwik Kowalski