In this paper, we present an improved Coulombianbased analytical calculation of magnetic fields created by permanentmagnetic rings. The 3 dimensional (3D) components of two types of magnetized rings (axially and radially) were analytically evaluated. The obtained components of the magnetic field are expressed over complete elliptical integrals of the first and second kind, as well as by Heuman's Lambda function. These expressions permit fast and accurate calculations of the magnetic field at any point of interest, for both regular and singular cases. The presented method gives an improvement of already known expressions for calculating the magnetic fields of the aforementioned magnetized rings, and we consider that these improved analytical expressions are more extendable to numerical applications.
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