The text shows that the electric field of a point electric dipole at the origin with moment p(t) = p(t)ẑ produces an electric field (away from the source) in cylindrical coordinates of the form

where

The family of curves R(ρ, z) = const. = R₀ may be interpreted as electrical field lines.
(a) Show that the points (ρ, z) of null (zero) electric field where the field lines pinch off and detach from the source at time t satisfy

(b) Assume that p(t) = p₀ cos ωt and show that only those field lines with |R₀| 0/c √3 can detach from the source. Check that the detachment-point solutions correspond to ρ > 0.

Transcribed Image Text:

E(p, z, t) = 1 dR, -2 1 4περ [ρ dρ 1 dR -ô p dz