The self and mutual-inductance of linear conductors . TraS^ — I 2a cos 6. 2ad6 — /^ .: 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). Fig. 20. For the entire area of the circle with respect to the point P •. S,^d+- (54) a If d= <9, Sj^ = —, the value for the area of the circle with respect to2 the center of the circle. For the area of a circle with respect toitself, the a. m
The self and mutual-inductance of linear conductors . TraS^ — I 2a cos 6. 2ad6 — /^ .: 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). Fig. 20. For the entire area of the circle with respect to the point P •. S,^d+- (54) a If d= <9, Sj^ = —, the value for the area of the circle with respect to2 the center of the circle. For the area of a circle with respect toitself, the a. m. s. d., S/ would be found byintegrating P^Pl = r^-\-r^—2 r^r^ cos {0^—0^twice over the area of the circle. This was done in effect by Wien^^ in get-ting his formula for the self-inductance of acircle, which is a little more accurate thanthe formula deduced by the use of geometrical ^ mean distances only, when the geometrical mean distances are usedfor the arithmetical mean distances. These examples are sufficient to illustrate the differences in thevalues of the geometrical mean distances and the arithmetical mean 12 M. Wien: Wied, Annal. 53, p. 928, 1894.
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