Answer Happy

Problem 10.2. A lattice of dipoles = A simple cubic lattice of lattice constant a is an array of points located at the points (x, y, z) = (nx a, ny a, nz a) , where the {nx, Ny, nz} are a set of any three integers. Such a lattice is shown in the figure below. In a simple cubic crystal, identical molecules are located at these lattice points. Consider a simple cubic crystal of molecules, all of which have the same in magnitude and direction) dipole moment Ē. Let us fix our attention on one particular molecule, call it j. It is evident that it has six nearest neighbors at distance a, twelve next-nearest neighbors at distance V2 a, and so on. Find the electric field at j due to the six moments on its six nearest-neighbor molecules for an arbitrary orientation ofp. Hint: A useful choice of coordinates is to let the lines joining j to its nearest neighbors define the x, y, and z axes. Simple Cubic Lattice