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 the electric potential and force between cylindrical conductors.
| Identifier | ExFiles\Box 54\3\ Scan233 | |
| Date | 16th July 1924 | |
| EFC1/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 e = V / (2 log_e (b/a)) Hence the electric force at radius r 2e/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 force V / (a log_e (b/a)) just off the surface of the wire, may increase or diminish as a increases, according to circumstances. Contd. | ||