The self and mutual-inductance of linear conductors . hence the actual self-inductance of such a cir-cuit is not the value of the self-inductance given byequation (9). The latter is the self-inductance of a part of a closed circuit due tothe current in itself. The actual self-inductance of any closed cir-cuit of which it is a part will be the sum of the self-inductances ofall the parts, plus the sum of the mutual inductances of each oneof the component parts on all the other parts. Thus the self-inductance of a rectangle is the sum of the self-inductances of thefour sides (by equation 10) plus
The self and mutual-inductance of linear conductors . hence the actual self-inductance of such a cir-cuit is not the value of the self-inductance given byequation (9). The latter is the self-inductance of a part of a closed circuit due tothe current in itself. The actual self-inductance of any closed cir-cuit of which it is a part will be the sum of the self-inductances ofall the parts, plus the sum of the mutual inductances of each oneof the component parts on all the other parts. Thus the self-inductance of a rectangle is the sum of the self-inductances of thefour sides (by equation 10) plus the sum of the mutual inductances of I and 3 on each other,and of 2 and 4 on eachother (taking account ofsign the mutual induct-ances will be negative).Since the lines of force dueto side I in collapsing donot cut 2 and 4, the mutualinductance of i and 3 on 2and 4 is zero. In a recent number of theElektrotechnische Zeit-schrift,* Wagner that the total magnetic flux of a finite straight conductor as derived from the Biot-Savart X-i —B. >^ L law has an infinite value, andance is therefore infinite and concludes thathence that one can the self-induct-properly *Karl Willy Wagner, Elek. Zeit., July 4, 1907, p. 673. 312 Bulletiii of the Bureau of Standards. \ Vol. 4, No. 2. Speak of the self-inductance only for closed circuits. In reach-ing this conclusion he takes the integral expression given bySumec ^ for the flux through a rectangle of length y and breadthx^—x^ due to a finite straight wire of length /, as shown in Fig. then lets the rectangle expand, x.^ being constant, and the ratioyjxc^ remaining constant until Xc^ and y are both infinite. This givesan infinite value to the flux, but does not prove the self-inductanceof the finite wire AB to be infinite, defining the self-inductance as Ihave done above. When the current in the wire decreases, the fieldeverywhere decreases in intensity, and we think of the lines as collaps-ing upon the wire; that is, mo
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