Usually, to obtain the dielectric constant of materials, one must measure the capacity increment of condenser due to the insertion of materials between its plates. Especially, in the case of the assemblage of fibers, the increment of capacity is much dependent upon the distribution of fiber direction. In the present paper, the author marks this point, and calculates the capacity increment by approximation. Some of the results are as follows:
1) When each fiber is perpendicular to the plate, the rate of capacity increment
ΔC/
C0 becomes
2) When the fibers are parallel each other and to the plate, the rate of increment becomes
3) When the distribution functions are as follows: a)
f(θ)=sinθ (where θ is the angle between the fiber and the normal of the plate), the rate of increment becomes b)
f(θ)=
constant (i.e., the direction of fiber is completely at random), the rate of increment becomes
Where
ΔC is the capacity increment due to the insertion of materials,
C0 is the capacity of air filled condenser, ε is the dielectric constant of specimen, and ξ is the volume fraction of materials.
The experimental data, presented in this paper, show a very good agreement with the theory.
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