1. Presentation File: Additional materials 12Aug20111CMDAYS 2011 Aravamudhan http://www.ugc-inno-nehu.com/cmdays_abstract_accepted.html Download Presentation File for CMDAYS2011 oral presentation

2. Magnetic Field Vector Vector map representation of Homogeneous magnetic Field. The scales should be so chosen that the magnitude of the individual Vectors in the map above, is equal to the Magnitude of the Vector in the line Vector representation. The individual vector magnitude should not be multiplied by the number of such vectors to equal the total magnetic field strength. HOMOGENEOUS Magnetic Field An inhomogeneous magnetic field can be more conveniently represented by the Vector Maps of mathematics A HOMOGENEOUS FIELD can be adequately represented by a Line VECTOR, but inhomogeneous field is represented well by the VECTOR MAP. See in the next slide illustrations of various distribution functions in Vector Maps 12Aug20112CMDAYS 2011 Aravamudhan Magnetic Field representation by Lines of Force If the | H | field is an externally applied HOMOGENOUS field the strength of which is known by the intensity in Vacuum, then the corresponding | B | field is inclusive of the magnetization within the sample. If Magnetization is defined as the induced magnetic moment per unit volume calculable from the volume susceptibility, the resultant of H & M, then if the magnetization is NOT HOMOGENEOUS, B would not be homogeneous, and the Vector Map representation would consist of Vectors of varying lengths over the extent of the sample.

3. http://mathworld.wolfram.com/VectorField.html Magnetization can be described also by Vector Maps and these Vector maps may not be called Vector Fields The question framed as the title of the abstract can be reframed as whether, the Vectors constituting the Vector maps represent interacting Moments? The question of interacting vectors of the Vector map may still be confronting, if the total magnetization vector magnitude is divided by the number of vector elements in the so that the total magnetization as the resultant of the vector elements 12Aug20113CMDAYS 2011 Aravamudhan

4. Line defined by Polar angle θ / direction of radial vector Polar angle intervals Δθ are half the values of the corresponding intervals on the left. The Vector Map representation for the divided magnetic moments and their distribution as per the criterion stipulated for the improved validity of point dipole approximation enabling the discrete summation to replace the integrals. The vector elements represent moments and not a field S N The induced field calculations at a point Specifying the position coordinates for the plot of Vector map: described in next slide 16 Aug 20114S.Aravamudhan CMDAYS2011

5. Volume of the sphere at distance ‘R’ is (4/3)π r 3 = V s with r = C(a constant) x R R i+1 = R i + r i + r i+1 With “C= R i / r i, i=1, n” For a sphere of radius =0.25 units, and the polar angle changes at intervals of 2. 5˚ There will be 144 intervals. Circumference= 2π/4 so that the diameter of each sphere on the circumference = 0.0109028; radius = 0.0054514 C = R/r = 0.25 / 0.0054514 = 45.859779 [46.859779/44.859779] = 1.04458334 Log (1.0445834) = 0.0189431 (r/R) 3 =1.0368218e-5 =0.000010368218 R i+1 = R i ● (C+1) / (C-1) For a predetermined polar angular co-ordinates (θ, Φ), the distance along the radial vector R i+1 is calculated. Thus every vector in the Vector map can be specified by the vector magnitude | μ i,θ, Φ | (which is proportional to the Volume of the sphere with radius r i,θ,Φ ), position coordinates (r i,θ,Φ,θ,Φ) 16 Aug 20115S.Aravamudhan CMDAYS2011 Calculation of induced fields:http://www.ugc-inno- nehu.com/cmdays2011/0_1_10Aug2011.ppt

6. |μ i | = (4/3) π r i 3 · χ v · | H | with (r i ) K where subscript K specifies a (θ,Φ ) angular polar coordinate, The set of magnetic moments are mapped onto a Vector space with the Polar Coordinate space: This Vector Map is more complicated version than the examples of Vector maps displayed in slide-2. This magnetic moment map should in turn return the magnetized specimen shape accounting for the entire material content of the magnetized material, with appropriately filling the Voids between spheres by (drawing) describing a cubical volume enclosing the sphere around every sphere In place of each of the spherical element draw a Vector of appropriate magnitude ! That gives the Vector map of the Moments distribution 16 Aug 20116S.Aravamudhan CMDAYS2011