Question

The figure shows eight point charges arranged at the corners of a cube with sides of length d.  The values of the charges are +q and −q, as shown.  This is a model of one cell of a cubic ionic crystal.  In sodium chloride (NaCI), for instance, the positive ions are Na+ and the negative ions are CI.  (a) Calculate the potential energy U of this arrangement.  (Take as zero the potential energy of the eight charges when they are infinitely far apart.)  (b) In part (a), you should have found that U < 0.  Explain the relationship between this result and the observation that such ionic crystals exist in nature.

(HINT:  This is a configuration energy problem.  However, it is lengthy to solve.)

+q
+q
P
+4
+q

Image Transcription

+q +q P +4 +q

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Electric Charges and Fields

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