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3. Equivalence of uniform problems [4 points (seminar)] 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 in terms of polarization P, (iii) vector potential A in terms of magnetization M. b) Show that for p, P and M uniform, the definitions above all depend only on the integral I(F) = √₂ ª ř - ¹ |T_T¹|³ d³p²- 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 in terms of polarization P, (iii) the vector potential A in terms of magnetization M.