4. A charge density p(r. 1) and current density J(r.1) are localised inside a region V so that p and J both vanish on th
Posted: Thu Feb 17, 2022 11:08 am
4. A charge density p(r. 1) and current density J(r.1) are localised inside a region V so that p and J both vanish on the surface of V and everywhere outside V. Show that dp 5, Jar = dt where p is the electric dipole moment for the volume V. [Hint: You may find it useful first to show 2(x,J)) = J,+x(V.J), where r has components x; Recall the continuity equation involving p and J and the definition p = Srpſr)dr for the dipole moment in volume V.]