Field magnetic

Typical uses Separation of ferro- and paramagnetic materials such as minerals and ceramics. 

Typical particle size and feed concentration range 40-4000 pm and 5-20% w/w (LIMS or HIMS), 400 pm and 10% w/w (HGMS). 

Assume that the volume D is filled now with magnetic masses with the intensity of magnetization I(r). It is well known that the corresponding magnetic field H(r ) can be represented as follows (Zhdanov, 1988)  

The important common feature of both gravity and magnetic forward problems is that operators A- (p ) and A ) are linear operators. Therefore the inverse problem operators (A ) (g) and (.4 ) (H) are also linear. We will study carefully the properties of linear operators in Appendix B. We will see below that linear inverse problems have many important features that simplify their solution. 

In order to interpret the g-values associated with spin resonance experiments, it is therefore necessary to construct the matrix of -f- 2s within the basis set ij i and t i- This construction is facilitated by the prior calculation of matrix elements of + 2s within the set of d-orbitals (Eqs. 4). The matrix elements of /z -f- 2sz are easily calculated, those of /x + 2sx and -(- 2sy are best handled by means of the shift operators (Eqs. 75) and the defining relations given by Eqs. (12). The resulting matrices are given in Table 13. The conversion of the matrices to the basis set t], is then accomplished by means of Eqs. (48), and are given in Table 14. Finally the matrices of -f 2s in the basis set 4 t. J l are computed (Table 15). 

The eigenvalues of /x + 2sx and + 2sy are obtained from the solution of the secular determinant associated with the corresponding matrices in Table 15. They are 

Inserting the observed g-values into Eqs. (89) and requiring that 

It is assumed, and borne out by subsequent calculation, that the observed g-values are associated with the splitting of the lowest Kramers doublet. Therefore the numerical values of the coefficients in Eqs. 

We note that the coefficient of %+ in (or the coefficient of 5 in ( i) has an absolute value close to unity so that the lowest Kramers doublet closely resembles the -orbital. The departure from exact correspondence or the reason for the appearance of the terms in vj and is due to spin-orbit coupling. Thus the main effect of spin-orbit couphng 

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Gouy balance A balance for the determination of magnetic susceptibility. The sample is weighed in and out of a magnetic field and the susceptibility is calculated from the difference in weights. 

Hall effect If a current (I) is passed through a conducting crystal in a direction perpendicular to that of an applied magnetic field (H), the conductor develops a potential (V) between the faces which are mutually perpendicular to both the direction of the current and the magnetic field. This is known as the Hall effect the magnitude of the potential difference is given by... 

The source is brought to a. positive poteptial (I/) of several kilovolts and the ions are extracted by a plate at ground potential. They acquire kinetic energy and thus velocity according to their mass and charge. They enter a magnetic field whose direction is perpendicular to their trajectory. Under the effect of the field, Bg, the trajectory is curved by Lorentz forces that produce a centripetal acceleration perpendicular to both the field and the velocity. 

Table 3.9 gives the resonance frequencies in a 9.4 tesla magnetic, field. . . 

The sample is placed in a cqnst a nt magnetic field, Bq, and the variation in frequency throughout the t/omain Tieing expfored excites one by one the different resonances. The scan lasts a few minutes. Inversely, one can maintain a constant frequency and cause the magnetic field to vary. 

The sample is again subjected to a constant magnetic field but all the nuclei are excited by a very short radio frequency pulse. The frequency e (e.g., 400 MHz for a proton at 9.4 tesla) is applied over a period of several... 

The principle physical phenomenon of applying the eddy current method for evaluating the amount of residual austenite in the structure of quenched steel is magnetic induction, involving the influence of the changeable magnetic field on the studied area, found under the probe. 

In effect of such activity eddy currents in the studied area are induced, producing own magnetic fields which following Lenz s rule are directed adversely to the induction field this decreasing its intensity (Fig. 1). 

The intensity of the magnetic field produced by eddy current is depended on electrical conductivity and magnetic permeability of the studied area. In case of a uniform structure, when the conductivity of the material is high, the intensity of the induced magnetic field is big and signal received by probe Hp is small. 

Structure defects decrease conductivity of the studied material, and then the intensity of the induced magnetic field is small and the signal received by the probe Hp is big (Fig.2). Low conductivity of austenite is a defects of the structure in case of residual austenite in the martensite structure, which with regard to the magnesite structure is as 1 5. Eddy currents produced in the studied area are subject to excitation in effect of small conductivity of austenite grains in the structure of the studied material. 

TRIFOU is a combined Finite Elements/Boundary Integral formulation code. The BIM formulation in vacuum is suitable for NDT simulation where the probe moves in the air around the test block. The FEM formulation needs more calculation time, but tetrahedral elements enable a large variety of specimens and defect geometries to be modelled. TRIFOU uses a formulation of Maxwell Equations using magnetic field vector h, where h is decomposed as h = hs + hr (hj source field, and hr reaction field). 

A SQUID [2] provides two basic advantages for measuring small variations in the magnetic field caused by cracks [3-7]. First, its unsurpassed field sensitivity is independent of frequency and thus dc and ac fields can be measured with an resolution of better than IpT/VHz. Secondly, the operation of the SQUID in a flux locked loop can provide a more than sufficient dynamic range of up to 160 dB/VHz in a shielded environment, and about 140 dB/>/Hz in unshielded environment [8]. 

It must be admitted that eddy currents are a little unmanageable, they tend to flow where they want as soon as the magnetic field leaves the probe, so we may not know for certain what a flaw is really like. 

The sensibility to defects and other testing parameters of pieces can be modified by the geometry of the piece to be controlled and the conception of the probe. It is sufficient to set the direction of circulation of eddy currents, regulate the magnetic field intensity and choose the coil of the appropriate size. 

To decrease the contact surface (to assimilate it to a point) by the focalization of the magnetic field. 

It is a probe whose the coil support is a small circular sticks with a straiglit section. The aim of our study is to assimilate the resulting magnetic field to a material point, hi order to minimize the lateral field, we have chosen the construction of conical coil where the lateral field at a contact point in respect to a straight configuration is decreased with an exponential factor. The results obtained from the curves are as follow ... 

The first equation (1) is the equation of state and the second equation (2) is derived from the measurement process. Finally, G5 (r,r ) is a row-vector that takes the three components of the anomalous ciurent density vector Je (r) = normal component of the induced magnetic field. This system is non hnear (bilinear) because the product of the two unknowns /(r) and E(r) is present. 

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