Boundary-Value Problem for Electromagnetic Fields in Cylindrical Conductor with Circumferential Electrodes Excited by AC-Current

The bounardy-value problem for the electromagnetic fields E(r, t) = {Er (r, z, t),0, Ez (r, z, t)} and B(r, t) = {0, B (r, z, t),0} in an electrically conducting cylinder of radius r = a and infinite length (-∞≦z≦+∞) is treated, which are excited by a periodic ac-current I(t) = I cosωt entering and leaving the cylinder through circumferential electrodes at r = a and z = ± c. Solutions for E(r, t ) and B(r, t) are obtained in terms of Fourier integrals which are reduced to infinite series by means of the residue theorem. Graphical presentations of the fields E(r, z, t) and B(r, z, t) versus z and r for times ωt = 0 and π/2 are given which show the relative amplitude and phase relations of the fields. An application of the results to medical physics is discussed concerning the measurement of the electrical conductivity of the tissue of limbs.