(a)What is the electric potential generated by the charge distribution given below? a p(r) = b°2;8(r) = b' 8(r). axi = H

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A What Is The Electric Potential Generated By The Charge Distribution Given Below A P R B 2 8 R B 8 R Axi H 1 (106.05 KiB) Viewed 72 times

(a)What is the electric potential generated by the charge distribution given below? a p(r) = b°2;8(r) = b' 8(r). axi = Here bi is a constant vector. Explain the multipolar structure of this source. (b) Now instead of sitting still at the origin, suppose the position of the singular source oscillates sinusoidally, along the ż axis, with semi-amplitude d, at frequency w, starting at the origin at time t = 0. What is the appropriate expression for p? (c) Give the conditions (i) for this source to be non-relativistic, and (ii) to be in the wave zone of this source. In the wave zone and in Lorenz gauge, what is (iii) the leading dependence on radius r, and (iv) the lowest non-vanishing term (monopole, dipole, etc.) in the multipole expansion of the Lorenz-gauge expression for the potential V(t, r)? (d) In the wave zone, give the potential V(t, r) (in Lorenz gauge), stopping at the first nonvanishing term in the multipole series.