18
KINETIC ENERGY OF ELECTRICITY IN MOTION [I]
If here we calculate the constant term directly and expand
the remaining terms in descending powers of n, we find the
second part to be
0.18848+ log n—
1
7
-
8n 192n2
The sum of both parts gives the required term
=
4
3
0.43848+ log 8 √(2) + 1928²
n
=
= log({1-5503
(2)"}+
3
192n2
3
=n log√5.7773n·
n log(5-7773m-2} +192m³...
and hence to a considerable degree of approximation the self-
inductance of a single layer becomes
4n
II = 45m + + log 29 $5.7773m).
Π 4Sn{
RT
For large values of n the root involved in this expression
rapidly converges to unity, so that for such values of n we
may write more simply
II
=
4Sn{++ log 22}
We get this approximation at once by calculating the
induction of the whole arrangement on one of the middle
wires, and assuming it true for all the wires. We may use
this simpler method in calculating the mutual inductance of
two different layers.
Let e be the perpendicular distance between two layers,
and suppose that in them the individual pairs of wires are so
placed that the wires traversed in the same direction are
opposite, with their axes in one plane perpendicular to the
two layers. Then the mutual inductance of one layer and a
median wire of the second layer is