Problem 4 The figure shows a point charge q at the center of two concen- tric thin shells. The inner shell has radius a and surface charge density a; the outer shell has radius b and surface charge den- sity σb. (a) Write Gauss' Law in the special form appropriate for spherical symmetry. (b) Compute the electric field in region I (see figure) (c) Compute the electric field in region II. (d) Compute the electric field in region III. III II q a

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Ising model of Ferromagnets

The Ising model is one of the easiest and most famous theoretical models for ferromagnetism in statistical mechanics. When a group of atomic spins aligns such that their magnetic moments are pointed in the same direction and produce a strong permanent magnetic moment in macroscopic size, the phenomenon is called ferromagnetism. The relative permeability of these magnets is greater than unity and increasing magnetization with the applied external field. Even in the absence of an external magnetic field, these substances retain spontaneous magnetization. An example of ferromagnets is iron.