Use the result of Prob. 10.34 to determine the power radiated by an ideal electric dipole, p(t), at the origin. Check that your answer is consistent with Eq. 11.22, in the case of sinusoidal time dependence, and with Prob. 11.26, in the case of quadratic time dependence
\langle P\rangle=\int\langle S \rangle \cdot d a =\frac{\mu_{0} p_{0}^{2} \omega^{4}}{32 \pi^{2} c} \int \frac{\sin ^{2} \theta}{r^{2}} r^{2} \sin \theta d \theta d \phi=\frac{\mu_{0} p_{0}^{2} \omega^{4}}{12 \pi c} (11.22)