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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 and explanations regarding the electric potential and force between a central wire and an outer conducting cylinder.

Identifier  WestWitteringFiles\M\2October1924-December1924\  Scan72
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 = [ -2e logₑ r ](from a to b)

i.e. V = 2e logₑ (b/a)

Hence the electric force at radius r

= e/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, 1/a diminishes, but 1 / (logₑ (b/a)) increases, so that the electric force

V / (a logₑ (b/a))

just off the surface of the wire, may increase or diminish as a increases, according to circumstances.

Contd.
  
  


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