MEASUREMENT OF DIELECTRIC AND MAGNETIC PROPERTIES 445 



saturated region. ^Measurements of single crystals and of resonance 

 curves with this method have not yet been made. 



It is anticipated that in both cases smaller and thinner discs would be 

 needed than have been available so far. However, it can be hoped that 

 these difficulties will be overcome in the near future and that the disc 

 method will be useful also for the study of ferromagnetic resonance 

 phenomena. 



Appendix 

 perturbation of a degenerate cylindrical cavity due to a thin 



DISC 



The general perturbation equation for a lossless cavity can be derived 

 from energy considerations or directly from Maxwell's equations. We 

 obtain for the shift of resonance frequency due to a small perturbation: 



^ / w-^* dv + - P-E'^^ dv u) , TT^ w 



c^o ,,, r -^ -. . . W'^' 



Jvi 



coo resonance frequency of the empty cavit}^ 



coi resonance frequency of the cavity after insertion of the perturbing 



sample 



h^ magnetic field intensity vector in the empty cavity 



E electric field intensity vector in the empty cavity 



vi volume of sample 



V2 volume of cavity 



* indicates the conjugate value 



The denominator in (Al) indicates the total energy TF^'^ stored in the 

 empty cavity at resonance, whereas the numerator is equal to the addi- 

 tional magnetic energy TF^^^^ and electric energy We^^ stored in the 

 perturbing sample. 



Equation (Al) is valid if the frequency shift is small. 



Aoj _ oji — 0)0 



coo 1 COo 



« 1 (A2) 



and if the field in the cavity remains essential!}' unchanged after insertion 

 of the sample. In order to apply (Al) to the determination of the tensor 

 components Xm and k we should attempt to satisfy three conditions: the 

 electric field should vanish at the sample, the magnetic field should be 

 normal to the static magnetic field, and the relationship between RF 



