Charged Right Circular Cylinder

Abstract

A new method permits the calculation of the electric field surrounding a charged conducting surface of revolution without the use of orthogonal functions. Detailed formulas show how to find the charge density on a right circular cylinder with any desired precision. The numerical examples worked out give the maximum deviation of the actual surface from that of a true cylinder of diameter d to be −0.0015d, −0.00037d, −0.00017d, +0.0016d, and +0.014d for length to diameter ratios ¼, ½, 1, 2, and 4, respectively. The capacitance calculation gives an accuracy of one part in 30 000 for the ratios ½, 1, and 2. A capacitance formula is worked out which is accurate to one part in 1000 over the ratio range 0 to 4. Additional formulas indicate the method of solution for the bodies in longitudinal and transverse electric fields and the extension of two‐body problems such as the thick plate parallel plate capacitor. A way to calculate the flow about bodies of revolution is indicated. Digital computers are well suited to this method as no function tables are needed.