We present results for the effective surface impedance tensor (EIT) of polycrystals of metals in a weak uniform magnetic field H. The frequency region corresponds to the region of the local impedance boundary conditions applicability. We suppose that the resistivity tensor rhoik(H) of single crystal grains out of which the polycrystal is composed, is known up to the terms O(H2). For olycrystals of metals of arbitrary symmetry elements of EIT can be calculated within the same accuracy in $H$, even if the tensor rhoik(H)is strongly anisotropic. As examples, we write down EIT of polycrystals of (i) cubic metals, (ii) metals with ellipsoidal Fermi surfaces, (iii) metals of tetragonal symmetry whose tensor rhoik(0) is strongly anisotropic. Although polycrystals are metals isotropic in average, in the presence of a uniform magnetic field the structure of EIT is not the same as the structure of the impedance tensor of an isotropic metal with a spherical Fermi surface.
The obtained results are exact in the framework of the approximation used when describing single crystal galvanomagnetic characteristics. They cannot be improved neither in powers of H, nor with respect to the anisotropy of single crystal grains.
We present nonperturbative results for the effective impedance of strongly inhomogeneous metals valid in the frequency region in which the local impedance (Leontovich) boundary conditions are applicable. The inhomogeneity is due to the properties of the metal and/or the surface roughness. If the surface of an inhomogeneous metal is flat, the effective surface impedance associated with the reflection of an averaged electromagnetic wave is equal to the value of the local impedance tensor averaged over the surface inhomogeneities. This result is exact within the accuracy of the Leontovich boundary conditions. As an example, we calculate the effective impedance
for a flat surface with a strongly inhomogeneous periodic strip-like local surface impedance. For strongly rough surfaces a similar approach allows us to calculate the ohmic losses and the shift of the reflected wave, if we know the magnetic vector in the vicinity of the perfect conductor of the same geometry. One-dimensional rough surfaces are examined. Particular attention is paid to the influence of the evanescent waves generatedand the difference between the elements of the effective impedance tensor relating to different polarizations of the incident wave. The effective impedance tensor associated with a one-dimensional lamellar grating is calculated.