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1. [60 pts] The volume charge density of a stationary electric point dipole po located at x = xo is - p(x) = -Po (3)(x xo). (a) Show that | A). A; A(x) 58(3x - x') d'r = -V. A(x)/x-xr; where A(x) goes to zero as [x] +sufficiently fast. (b) Verify explicitly that the total electric charge of this electric point dipole is zero. (c) Electric dipole moment p of an arbitrary charge configuration is generally defined as p= 1. xp(x) dx. V Verify explicitly that the electric dipole moment of this electric point dipole is po. (d) Calculate the electric scalar potential (x) and the electric field E(x) of this electric point dipole. 1. [60 pts] The volume charge density of a stationary electric point dipole po located at x = xo is - p(x) = -Po (3)(x xo). (a) Show that | A). A; A(x) 58(3x - x') d'r = -V. A(x)/x-xr; where A(x) goes to zero as [x] +sufficiently fast. (b) Verify explicitly that the total electric charge of this electric point dipole is zero. (c) Electric dipole moment p of an arbitrary charge configuration is generally defined as p= 1. xp(x) dx. V Verify explicitly that the electric dipole moment of this electric point dipole is po. (d) Calculate the electric scalar potential (x) and the electric field E(x) of this electric point dipole

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