The self and mutual-inductance of linear conductors . hat case being ) Z= 2(—) = microhenrys. These calculations are of course all based on the assumption of auniform distribution of current through the cross section of the con-ductors. For alternating currents in which the current density isgreater near the surface the self-inductance is less but the mutualinductance is substantially unchanged. ^ Rosa, this Bulletin, 3, p. i. ^ Its more exact value is , this Bulletin, 3, p. 9. Rosa.\ Inductance of Linear Conductors. Z^l 9. SELF-INDUCTANCE OF A SQUARE. The self-in
The self and mutual-inductance of linear conductors . hat case being ) Z= 2(—) = microhenrys. These calculations are of course all based on the assumption of auniform distribution of current through the cross section of the con-ductors. For alternating currents in which the current density isgreater near the surface the self-inductance is less but the mutualinductance is substantially unchanged. ^ Rosa, this Bulletin, 3, p. i. ^ Its more exact value is , this Bulletin, 3, p. 9. Rosa.\ Inductance of Linear Conductors. Z^l 9. SELF-INDUCTANCE OF A SQUARE. The self-inductance of a square may be derived from the expres-sion for the self and mutual inductance of finite straight wires fromthe consideration that the self-in-ductance of the square is the sumof the self-inductances of the foursides minus the mutual induct-ances. That is, L^^L^ — \M the mutual inductance of twomutually perpendicular sides beingzero. Substituting a for / and din formulae (9) and (12) we have T fi a^Ja^^p^L^—2a\ log —^—^ ^^ L P. Fie. 11. ?+=+-+^1 a a M— 2a\ log Neglecting /o7^^ a a V2 + i] A-^=2.[log^-^-^-^+ V2+, 2a ^_ ^1 ,-. Z = 4(A-J^) = 8a^log^-log,I±V^+^ ] (22) or Z = 8«(log- + ^—) r a {22a) where a is the length of one side of the square and p is the radiusof the wire. If we put /= 4^ = whole length of wire in the square, ^=2/(log -+^^—) or, Z= 2 /(log ~ — ), approximately. r (23) 318 Bulletiit of the Bureau of Standards. [Voi. 4, no. 2. Formulae (22) and (23) were first given by Kirchlioff^ in a—\oo cm, p — o.\ cm, we have from (22) Z=8oo (logg 1000—)= 5107 cm = = .o5 cm, Z= 5662 cm = microhenrys. That is, the self inductance of such a rectangle of round wire isabout 11 per cent greater for a wire i mm in diameter than for one2 mm in diameter. If l\p is constant, L is proportional to /. That is, if the thickness of the wire is proportional to the lengthof the wire in
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