A radial gap type rotating electrical machine comprising: a field which has permanent magnets forming a predetermined number of magnetic poles and which rotates on a rotation axis as a center; and an armature facing the permanent magnets through a cylindrical gap in a direction perpendicular to the rotation axis and having a number of teeth more than the predetermined number of magnetic poles and an armature coil concentrated-wound around a winding portion of the teeth, wherein the field further includes a magnetic ring which is provided at a position farther from the armature than the permanent magnet and which serves as a back yoke of the permanent magnet, and the magnetic ring includes a recess, a thickness of which in a radial direction around the rotation axis as a center comes to locally thin at a magnetic pole center which is a center in a circumferential direction with respect to the rotation axis of the magnetic poles, wherein a thickness of the magnetic ring in the radial direction takes a constant value except in the vicinity of the magnetic pole center, characterised in that a product of a length (b) of a thin region in the circumferential direction where the magnetic ring comes to the thinnest in the vicinity of the magnetic pole center and a value obtained by subtracting a thickness (t) of the thin region in the radial direction from the constant value is defined as a first value, a product of the constant value and a value obtained by dividing a length of the magnetic ring in the circumferential direction on the side of the permanent magnet in the circumferential direction by the predetermined number of magnetic poles is defined as a second value, and a ratio (β) of the first value to the second value is 5% or more. a field which has permanent magnets forming a predetermined number of magnetic poles and which rotates on a rotation axis as a center; and an armature facing the permanent magnets through a cylindrical gap in a direction perpendicular to the rotation axis and having a number of teeth more than the predetermined number of magnetic poles and an armature coil concentrated-wound around a winding portion of the teeth, wherein the field further includes a magnetic ring which is provided at a position farther from the armature than the permanent magnet and which serves as a back yoke of the permanent magnet, and the magnetic ring includes a recess, a thickness of which in a radial direction around the rotation axis as a center comes to locally thin at a magnetic pole center which is a center in a circumferential direction with respect to the rotation axis of the magnetic poles, wherein a thickness of the magnetic ring in the radial direction takes a constant value except in the vicinity of the magnetic pole center, characterised in that a product of a length (b) of a thin region in the circumferential direction where the magnetic ring comes to the thinnest in the vicinity of the magnetic pole center and a value obtained by subtracting a thickness (t) of the thin region in the radial direction from the constant value is defined as a first value, a product of the constant value and a value obtained by dividing a length of the magnetic ring in the circumferential direction on the side of the permanent magnet in the circumferential direction by the predetermined number of magnetic poles is defined as a second value, and a ratio (β) of the first value to the second value is 5% or more.