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).
Calculation of excess potential and electric force between a central wire and an outer cylinder.
| Identifier | ExFiles\Box 4\5\ 05-page291 | |
| Date | 16th July 1924 | |
| EPCL/T16.7.24. -2- Contd. The excess of potential (V) of the central wire over that of the outer conducting cylinder will then, by the definition of potential (as work done on unit charge) be - ∫ [from b to a] (2e/r) dr = [ 2 e log_e r ] [from a to b] i.e. V = 2e log_e (b/a) Hence the electric force at radius r = e/r = V / (2 log_e (b/a)) = V / (r log_e (b/a)) At radius a, i.e. just off the surface of the wire it is V / (a log_e (b/a)) and at radius b it is V / (b log_e (b/a)) The former of the two is the larger, because a is smaller than b. If while b and V are constant a increases, 1/a diminishes, but 1 / (log_e (b/a)) increases, so that the electric for V / (a log_e (b/a)) just off the surface of the wire, may increase or diminish as a increases, according to circumstances. Contd. | ||