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Dipole Interactions

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4. (a) If r denotes the position vector whose ith component is xi and b is a constant vector whose ith component is bi; use Cartesian tensor methods to prove that
{Please refer to the attachment}.

(b) The mutual potential energy associated with two dipoles of moments vector_b and vector_c is given by {Please refer to the attachment} where vector_r is the position vector of one with respect to the other and vector_b and vector_c are constant vectors. Prove that
{Please refer to the attachment}.

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Solution Summary

We derive some formulas involving dipole interactions. Cartesian tensor methods to prove the given entity are used.

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