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##### Letbe a harmonic function On the annulus{2 â‚¬ Cla < Izl < b}.Show that there is a constant C such that u(z)_ C In |-l has a harmonic conjugate On the annulus_ Show that this constant is du C (reio ) do 2T dr where r â‚¬ (a,6).
Let be a harmonic function On the annulus {2 â‚¬ Cla < Izl < b}. Show that there is a constant C such that u(z)_ C In |-l has a harmonic conjugate On the annulus_ Show that this constant is du C (reio ) do 2T dr where r â‚¬ (a,6)....
##### Two identical spheres with mass m are hung from silk threads of length L $\textbf{(Fig. P21.62).}$ The spheres have the same charge, so $q_1 = q_2 = q$. The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. Show that if the angle $\theta$ is small, the equilibrium separation $d$ between the spheres is $d = (q^2L/2\pi\epsilon_0 mg)^{1/3}$. ($Hint$: If $\theta$ is small, then tan $\theta \cong sin \theta$.)
Two identical spheres with mass m are hung from silk threads of length L $\textbf{(Fig. P21.62).}$ The spheres have the same charge, so $q_1 = q_2 = q$. The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. Show that if the ang...