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 calculations for electric potential and force between a central wire and an outer cylinder.
| Identifier | ExFiles\Box 54\3\ Scan255 | |
| Date | 16th July 1924 | |
| EFCl/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 logₑ r ](from a to b) i.e. V = 2e logₑ (b/a) Hence the electric force at radius r = 2e/r = V / (2 logₑ (b/a)) = V / (r logₑ (b/a)) At radius a, i.e. just off the surface of the wire it is V / (a logₑ (b/a)) and at radius b it is V / (b logₑ (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, b/a diminishes, but 1 / (logₑ (b/a)) increases, so that the electric forc V / (a logₑ (b/a)) just off the surface of the wire, may increase or diminish as a increases, according to circumstances. Contd. | ||