The electrostatic field in the neighborhood of a slender, axisymmetric conductor is expanded in prolate‐spheroidal harmonics to obtain approximations to the capacitance, the dipole moments induced by both axial and transverse fields, and the induced charge on a grounded boss in a uniform field. The capacitance calculated for a right‐circular cylinder with &dgr;=diameter/length<1 is found to be within 5% of the more accurate results calculated by Smythe. The corresponding comparisons for the dipole moments and the induced charge on a cylindrical boss are less impressive for non‐small &dgr; but suggest the general utility of the slender‐body approximation for &dgr; of the order of 10−1or less.