From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Page of mathematical analysis concerning electric force and potential difference in relation to wire diameter.
| Identifier | ExFiles\Box 54\3\ Scan234 | |
| Date | 1st July 1924 | |
| EFGL/T16.7.24. -3- Contd. The two effects balance one another if d/da{Bernard Day - Chassis Design} (a logE b/a ) is zero. This is the case if a . -b/a^2 + logE b/a = 0 if logE b/a = 1 i.e. if b/a = E b = Ea or a = 1/E b It is clear therefore that for variation of a (b constant) the minimum electric force at the surface of the wire for a given potential difference V occurs when a = 1/E b and is V/a or E/b V . If a is less than this value and increasing, the electric force is diminishing, and if a is more than this value and increasing, the electric force is increasing. (When the wire is small in diameter, the electric force is greater because of the sharper radius, and when the wire is of diameter approaching that of the outer conducting cylinder, the electric force is again greater, due to the reduced radial distance from that conductor). Hence, when a is less than the critical value, increasing the effective wire diameter, such as occurs if a brush discharge takes place, relieves the electric stress. Consequently with sufficient potential on the wire, a brush discharge is possible without a spark taking place. (N.B. It is interesting to note that for a given outer radius b, and a given bearable electric stress R, the maximum potential difference withstandable by the gap is Rb{R. Bowen}/E and occurs when the central wire is of radius b/E ). Contd. | ||