The self and mutual-inductance of linear conductors . m. d. and a. m. s. d. inthe third term; that is, a term of the form Si log R, To get this we must integrate as follows: .^[log(.-.)-g+flog.-g (46) I f & I f 6 d^S^^ log i^2 = - I (^ —-;i:)^log {d—x)dx-r-^ I x^ log xdx I (b — xYdx I x^dx 9J0 9J0 6V ^ 12; (47) i^ogb-1^^ (48) ^/logi?, = |, We may now substitute in (39) as follows: -?log<3^=log^—- ^ d^— —^ 2 3(3^^ log <^=—(log ^—^ j 330 This gives Bulletin of the Bureau of Standards. ivoi. 4, no. 2^ L — AfiTa— /.ira I^ + 3&) ^°^ ^^-^^ ^-h (°^ -^2) -^-9&] A 32«/ 1 8<3; log- -^ ^ b —1
![The self and mutual-inductance of linear conductors . m. d. and a. m. s. d. inthe third term; that is, a term of the form Si log R, To get this we must integrate as follows: .^[log(.-.)-g+flog.-g (46) I f & I f 6 d^S^^ log i^2 = - I (^ —-;i:)^log {d—x)dx-r-^ I x^ log xdx I (b — xYdx I x^dx 9J0 9J0 6V ^ 12; (47) i^ogb-1^^ (48) ^/logi?, = |, We may now substitute in (39) as follows: -?log<3^=log^—- ^ d^— —^ 2 3(3^^ log <^=—(log ^—^ j 330 This gives Bulletin of the Bureau of Standards. ivoi. 4, no. 2^ L — AfiTa— /.ira I^ + 3&) ^°^ ^^-^^ ^-h (°^ -^2) -^-9&] A 32«/ 1 8<3; log- -^ ^ b —1 Stock Photo](https://c8.alamy.com/comp/2AM5AP2/the-self-and-mutual-inductance-of-linear-conductors-m-d-and-a-m-s-d-inthe-third-term-that-is-a-term-of-the-form-si-log-r-to-get-this-we-must-integrate-as-follows-log-gflog-g-46-i-f-i-f-6-ds-log-i2-=-i-ilog-dxdx-r-i-x-log-xdx-i-b-xydx-i-xdx-9j0-9j0-6v-12-47-iogb-1-48-logi-=-we-may-now-substitute-in-39-as-follows-loglt3=log-d-2-33-log-lt=log-j-330-this-gives-bulletin-of-the-bureau-of-standards-ivoi-4-no-2-l-afita-ira-i-3-h-2-9-a-32-1-8lt3-log-b-1-2AM5AP2.jpg)
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The self and mutual-inductance of linear conductors . m. d. and a. m. s. d. inthe third term; that is, a term of the form Si log R, To get this we must integrate as follows: .^[log(.-.)-g+flog.-g (46) I f & I f 6 d^S^^ log i^2 = - I (^ —-;i:)^log {d—x)dx-r-^ I x^ log xdx I (b — xYdx I x^dx 9J0 9J0 6V ^ 12; (47) i^ogb-1^^ (48) ^/logi?, = |, We may now substitute in (39) as follows: -?log<3^=log^—- ^ d^— —^ 2 3(3^^ log <^=—(log ^—^ j 330 This gives Bulletin of the Bureau of Standards. ivoi. 4, no. 2^ L — AfiTa— /.ira I^ + 3&) ^°^ ^^-^^ ^-h (°^ -^2) -^-9&] A 32«/ 1 8<3; log- -^ ^ b —1 28^J (49) which is Rayleighs equation (43). This confirms the values of thequantities Sg^ and Sg^logRg employed in deducing the equation(49) from the formula (44) for M for two parallel circles. 17. ARITHMETICAL MEAN DISTANCES FOR A CIRCLE. The arithmetical mean distance of any point P on the circumfer-ence of a circle from the circle is found by integrating around thecircumference. Thus, since PB = 2<^ cos 6. TraS^ — I 2a cos 6. 2ad6 — /^a4.a .: S, = IT (50) Since the a. m. d. is the same for every pointof the circle we have also Fig. 19. s, = 4^ TT (51) For the arithmetical mean square distance we have nraS^ i 4^ 2 PB = a^--d^-{-2ad COS 6S, = a I {a--d-^2adcose)d0 = 7ra(d^-i-a^ TT^O, = ..S, = d^a (53)