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In this modification of Slater’s cavity perturbation theorem the perturbed magnetic field is expressed as a Fourier series based on the unperturbed cavity modes. The discontinuity in the field (hence the current) at the perturbing surface is two times the normal mode sum. Mode coupling terms are defined, leading to a matrix whose eigenvalues are the perturbed resonance frequencies of the cavity. Further manipulations of this matrix yield the normalized wave function as the normal mode sum. This technique is illustrated by a calculation for ridge waveguide.