- I Would Greatly Appreciate Solutions With Full Working For All Parts Of This Exam Question 1 (102.81 KiB) Viewed 38 times
I would greatly appreciate solutions with full working for all parts of this exam question.
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answerhappygod
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I would greatly appreciate solutions with full working for all parts of this exam question.
I would greatly appreciate solutions with full working for all parts of this exam question.
entral-prod-leet01-xythos.content blackboardedn.com - Printe A physical dipole consists of two charges Eq at r = ta, resulting in a dipole moment P =qa. a) Write down the electrostatic potential V(r) and calculate the electric field E() in all of space. Show that in the far field, r > a, the field is approximately 1 3(pºr)r - pr2 Er) = 4πέο 75 b) Consider this dipole in an external homogeneous field, Ehom Eoe. Write down the energy of the dipole in the field, and derive expressions for the force and torque on the dipole. What is the minimum energy configuration for the dipole? c) Now consider two physical dipoles p, and pg, whose moments (of equal magnitude) are perpendicular to their separation vector s. Carefully sketch the resulting electric field lines in the case where the dipoles are aligned parallel, and the case where they are antiparallel. In each case, what is the direction of the force between the dipoles, and why? d) For s = |a], the four point charges of the two dipoles are on the corners of square. For the antiparallel arrangment of the dipoles, write down the charge distribution p(r) using Dirac's 8-function, and use that to calculate the Cartesian components Qi; of the quadrupole tensor, given by а Quijs = % av dV (3rir; – dijr2)p(r). ?(. The quadrupole moment Q in direction î is given by Li; Qijrif;. Sketch the ex- trema and zeroes of Q on a circle in the plane of the charges.
entral-prod-leet01-xythos.content blackboardedn.com - Printe A physical dipole consists of two charges Eq at r = ta, resulting in a dipole moment P =qa. a) Write down the electrostatic potential V(r) and calculate the electric field E() in all of space. Show that in the far field, r > a, the field is approximately 1 3(pºr)r - pr2 Er) = 4πέο 75 b) Consider this dipole in an external homogeneous field, Ehom Eoe. Write down the energy of the dipole in the field, and derive expressions for the force and torque on the dipole. What is the minimum energy configuration for the dipole? c) Now consider two physical dipoles p, and pg, whose moments (of equal magnitude) are perpendicular to their separation vector s. Carefully sketch the resulting electric field lines in the case where the dipoles are aligned parallel, and the case where they are antiparallel. In each case, what is the direction of the force between the dipoles, and why? d) For s = |a], the four point charges of the two dipoles are on the corners of square. For the antiparallel arrangment of the dipoles, write down the charge distribution p(r) using Dirac's 8-function, and use that to calculate the Cartesian components Qi; of the quadrupole tensor, given by а Quijs = % av dV (3rir; – dijr2)p(r). ?(. The quadrupole moment Q in direction î is given by Li; Qijrif;. Sketch the ex- trema and zeroes of Q on a circle in the plane of the charges.
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