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

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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 1 (22.05 KiB) Viewed 65 times

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.]