Field cancelation

When the there are equal numbers of domains aligned in opposing directions, their magnetic fields cancel externally so the material appears not to be magnetized. 

When two dislocations get close together, much of their stress fields cancel out, especially if they are arrayed in a tilt-type grain boundary, or if they are the two ends of a small loop. Therefore if their strain energy fields were important in dissolution, isolated dislocations would etch more rapidly than those in boundaries. In fact they etch at almost identical rates (7), so again it may be concluded that the stress fields of dislocations have little effect cp dissolution at moderate undersaturations. 

It is necessary but not sufficient for an organic molecule to exhibit a large P to be an efficient SHG material. Such molecules must also pack in a crystal lattice in such a way as to result in an overall dipole moment. Polar molecules frequently crystallize in centrosymmetric crystalline structures in which the internal fields cancel. Thus, the search for the efficient organic nonlinear crystal is, in reality, a search for the polar crystal in which the macroscopic properties reflect the internal asymmetric molecular relation-... 

Returning to the strong field limit, the same gradient expansion at Eq. (B22) would lead to the result J/Ci = — (2P/B)B x VF, showing then that the strength of the magnetic field cancels out. However, the kernel Gp has two equal and opposite peaks away from the diagonal, and care may well be needed in... 

Note A quick diagnostic test for understanding a particular high-frequency conducted EMI problem (measured by a LISN at the inputs of the power supply) is to twist the output cables of the power supply tightly together (along with their respective return wires). This induces field cancellation (also called flux containment), thus reducing the radiation from the output cables (if present). 

FIGURE 2.2 A cathode ray tube with an electric field perpendicular to the direction of the cathode rays and an external magnetic field. The symbols N and S denote the north and south poles of the magnet. The cathode rays will strike the end of the tube at A in the presence of a magnetic field, at C in the presence of an electric field, and at B when there are no external fields present or when the effects of the electric field and magnetic field cancel each other. 

FIGURE 7.24 The (a) parallel and (b) antiparallel spins of two electrons. In (a) the two magnetic fields reinforce each other, and the atom is paramagnetic. In (bj the two magnetic fields cancel each other, and the atom is diamagnetic. 

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