Answer Happy

3. (a) Write down the definition of the electric dipole moment and define the elec- tric atomic polarisability a. Show how an expression for a in terms of the atomic volume may be estimated from Coulomb's law applied to an atom in an electric field. (b) Derive from first principles the expression for a torque arising on an electric dipole in an electric field. (c) Derive from first principles the expression for the net force on an electric dipole in an electric field. (d) Explain with the help of a sketch the concept of bound charge in matter and indicate where it resides. (e) Use the differential form of Gauss's law in free space, the concept of free and bound charges and the result that PBound = -V.P where P is the polarisation per unit volume, to derive the definition of the electric displacement field. Hence show how the Maxwell equation for Gauss's law may be rewritten for the case where matter is present. (f) Use the approximation of a linear dielectric to derive the relationship be- tween the electric susceptibility and the relative permittivity. (9) Use the differential form of Ampère's law in free space, the concept of free and bound current densities and the result that JBound = V x M to define the magnetic field H in terms of the magnetic field B and the magnetisation M. Hence show how Ampère's law may be rewritten for the case where matter is present. (h) Use the approximation of linear media to derive the relationship between the magnetic susceptibility and the relative permeability. (0) Write down Maxwell's equations in differential form, including Maxwell's cor- rection, for the case where media are present.