Answer Happy

Some physical situations are equivalent in the sense that they follow the same mathematical structure. This is the case in problems where the distribution of charge/polarization/magnetization is uniform (i.e. constant over a volume V that can have any shape). a) Recall the integral equations for the (i) electric field E in terms of charge density p. (ii) electric potential o in terms of polarization P, (iii) vector potential à in terms of magnetization M. b) Show that for p, P and M uniform, the definitions above all depend only on the integral デーデ I(F) = √√√ 4²7²7 |F-F1|³ where the integration is done over the volume V where the respetive quantity is constant. Use this to compute for a sphere of radius R (i) the electric field E in terms of charge density p. (ii) the electric potential o in terms of polarization P (iii) the vector potential A in terms of magnetization M.