The Spherical Coil as an Inductor, Shield, or Antenna

The spherical coil is an idealized form of inductor having, on a spherical surface, a single-layer winding of constant axial pitch. Its magnetic field inside is uniform and outside is that of a small coil or magnetic dipole. Its properties exemplify exactly some of the rules that are approximately applicable to practical inductors. Simple formulas are given for self-inductance, mutual inductance, coupling coefficient, effect of iron core, and radiation power factor in free space or sea water. This coil is the basis for evaluating the shielding effect of a closed conductive (nonmagnetic) metal shell. A special winding is described which enables simple and exact computation of self-resonance (the length of wire being just 1/2 wavelength in some cases).