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SOLVED: A useful mnemonic is that the operator ( ±) p ' grad [or ( ±) 𝐩 ·∇, if you prefer] converts monopole formulas into dipole formulas. For instance, the result of Problem 2-3 can be written 𝐅^(2)= (𝐩 ·grad) 𝐅^(1), where 𝐅^(1)=𝐄 is the force on a unit monopole charge, q=1. Show that this operator also works in the following cases: (a) field of a dipole 𝐄^(2)=-(p ·grad) 𝐄^(1) (b) potential of a dipole Φ^(2)=-(𝐩 · grad ) Φ^(1) (c) potential energy of a dipole U^(2)= (𝐩 ·. grad) U^(1)
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