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The accuracy of near-interaction (NI) evaluation is investigated for hypersingular and strongly singular kernels in solving electromagnetic (EM) integral equations. We first define the NI between a field point and a source triangular patch using a nearness factor (NF) and show the accuracy of numerical integrations for the NI integrals with hypersingular or strongly singular kernels. It is found that there exists a transition area or turning point before and after which the convergence behaviors of those integrations are greatly different. We define the NF value at the 1% relative error as the turning point NF 0 and define NF les NF 0 as the NI range. We find that NF 0=1.4 could be a bound of NI range for the triangles with a quality factor q > 0.35 and analytical formulas should be used in evaluating NI elements within the bound. Numerical examples for EM scattering by three-dimensional (3D) thin objects are used to demonstrate the significance of NI treatments for the accurate solutions.