The self and mutual-inductance of linear conductors . log I (64) Fig. 26. w here since the g. m. d. of the central conductor oneach of the others is a. The self-inductance of the return system is A = 2/ logf-^] a. log 2/—log {f\7ia ^) — I2/ log 2/ 1 a _ - I log --log (^^1^^^ ) + 1 4_ (65) A=2/M= Z=2/ For a = 2 cm, a^—i cm, ^0 = , ;/ = 6, /= 1000 cm Z=: 2000 log, 4-loge () + ^= 20oox microhenrys. If the inner conductor were surrounded by a very thin tube ofradius 2 cm for a return, in place of the six wires, the self-inductanceof the return circuit would be [? Z=2ooo
The self and mutual-inductance of linear conductors . log I (64) Fig. 26. w here since the g. m. d. of the central conductor oneach of the others is a. The self-inductance of the return system is A = 2/ logf-^] a. log 2/—log {f\7ia ^) — I2/ log 2/ 1 a _ - I log --log (^^1^^^ ) + 1 4_ (65) A=2/M= Z=2/ For a = 2 cm, a^—i cm, ^0 = , ;/ = 6, /= 1000 cm Z=: 2000 log, 4-loge () + ^= 20oox microhenrys. If the inner conductor were surrounded by a very thin tube ofradius 2 cm for a return, in place of the six wires, the self-inductanceof the return circuit would be [? Z=2ooo I log —\- a^ 4. (66) = 2000 X cm = microhenrys,a little greater than in the preceding case. Rosa. Inductance of Linear Conductors. 2>ll If the central conductor is also a multiple system, Guye hasshown ^^ how to find the mutual inductance of the two when thearrangement is symmetrical, the g. m. d. of the two systems beingderived by the aid of Cotess theorem. In this case log^,. = ^^log«-<0 or R,.,--=^(a,l — a;^J (67). Fig. 27. Thus, if a^^^2 cm, a^—\ cm, and ;/ = 6, 7?=: (64-if = and as n increases R^g approaches 2 as a limit, as it would be fortwo concentric tubes of radii i and 2. R^ and Rg for the two sepa-rate systems being given by (62) and R^^ b) (67), the self-inductanceof a return circuit with one system for the going current and theother for the return is readily calculated, being R 2 (68) These examples are sufficient to illustrate the calculation of theself and mutual inductance of multiple circuits b} the principle of the geometrical mean distance. 338 Bulletin of the Bttremc of Standards. [voi. 4, no. 2. 20. SELF-INDUCTANCE OF A NONINDUCTIVE WINDING OF ROUND WIRES. Suppose a to-and-fro winding of insulated wire in a plane, thelength of each section being /, the distance apart of the adjacent 5 1, 1 i - i4 j > I C/^ 1 I ? \o Fig. 28. wires, center to center, being d^ and the wire of radius p. Theresultant self-inductance of o
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