Average Forces in Electromagnetic Systems

Abstract

SummaryThe mechanical forces developed in electromagnetic systems are usually evaluated from surface integrals of the Maxwell stresses. For a large class of systems it is shown that the time average force can be expressed in terms of directly measurable circuittheory parameters. The system must be linear and loss free, but there is no restriction on the frequency of excitation.

Energy and Dispersion in Electromagnetic Systems

“…The results are obtained by considering the frequency dependence of the complex Poynting vector integrated over an enclosing mathematical surface. The surface integral expression obtained for the total energy is of the same form as that obtained in a discussion of average electromagnetic forces (Smith 1961) and may be reduced to impedance, admittance, and scattering matrix (Smith 1964a) forms in the same way.…”

“…Equation (l~) automatically accounts for all energy associated with the application of the electromagnetic field including any mechanical energy associated with the conduction or polarization processes. Some of the details of the following argument are similar to those used previously in deriving an expression for radiation-pressure forces (Smith 1961) …”

“…The surface integral in equation (24) is of the same form as that relating to average electromagnetic forces (Smith 1961) and may be reduced in the same ways (Smith 1961(Smith , 1964a. In the present paper no restriction to reciprocal media has been applied so that care is required in writing the reduced forms, as the scattering, impedance, and admittance matrices S, Z, and Yare not necessarily symmetric.…”

“…The equivalence of equations (26), (28), and (29) is a result of the relationships between admittance or impedance matrices and the scattering matrix (Montgomery, Dicke, and Purcell 1948;Smith 1964b). In terms of the reactance matrix X, iX being defined generally as the loss-free (antihermitian) part of Z, we have or (33) where B is the susceptance matrix related similarly to Y. Olearly X and Bare Hermitian in general, and real for reciprocal systems.…”

“…For loss-free systems the requirement that the complex power to the system be purely imaginary leads to the usual unitarity of S, that is S-1 = st, Equation (24) reduces to the following parameter matrix forms: (ii) Impedance and Admittance Matrix Forms (Smith 1961) …”