9780030839931, Chapter 27, Problem 2P

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Chapter 27, Problem 2P Problem Electric Field of an Arry of Indentical Dipoles with Identical Orientations, at a Point with Respect to Which the Array Has Cubic Symmetry The potential at r due to the dipole at r' is (27.82) By applying the restrictions of cubic symmetry to the tensor (27.83) and noting that = 0, show that E(r) must vanish, when the positions r' of the dipoles have cubic symmetry about r. Step-by-step solution Step 1 of 1 It is given that the potential at r due to the dipole at r' is Now, the electric field is equal to the gradient of the electric potential. Thus, = Here, is the unit vector along the electric field. It is given that the array of identical dipoles has cubic symmetry. So, it satisfied The above condition is valid for When the position r' of the dipoles have cubic symmetry about r, then r'=0 Putting the above value in the equation E Substitute 0 for in the above equation E(r)=0 Therefore, it shows that the electric field E(r) vanish when the position r' of the dipoles have cubic symmetry about r.