An Approximate Formula Giving The Capacity between Two Spindle-Shape-Electrodes Placed in Rotational Symmetry on a Straight Line

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This paper presents an approximate formula giving the capacity between two spindle-shaped electrodes whose axes are placed in a straight line, in rotational symmetry. The surfaces of electrodes are approximately represented by two cyclides μ=±μ_0=± constant in bi-cyclide coordinates (μ, ν, ψ). Laplace equation and its exact solution are given by Moon and Spencer. Though the potential function ℒ (μ, ν, ψ) is complicated, a simpler form of function may be obtained if the assumption ∂ℒ/∂ν=0 at any value of ν is approximately held. Under the approximate potential distribution, the capacity between two electrodes, C is obtained. C/aε_s=0.278/(√<kpq>)log_10|(√<k>(q-p)+√<pq>(k-1))/(√<k>(q-p)-√<pq>(k-1))| (pF/cm) where p=log_10|(1+snμ_0)/(1-snμ_0), and q=log_10|(1+k snμ_0)/(1-k snμ_0)| k; modulus a; a constant determining the size of electode ε_s; specific inductive capacity of the medium. The value of capacity has been calculated and their curves shown. To determine the capacity experimentally, measurements have been made for pairs of electrodes and the measured values agree fairly well with the calculated ones.
山梨大学の論文
1964-03-20