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Forums
Physics
Classical Physics
Help with Levi-Civita manipulation
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[QUOTE="user1139, post: 6446865, member: 680439"] [B]TL;DR Summary:[/B] Confused as to how I can obtain a divergence term by manipulating using Levi-Civita How do I write the following expression $$\epsilon_{mnk} J_{1n} \partial_i\left[\frac{x_m J_{2i}}{|\vec{x}-\vec{x}'|}\right]$$ back into vectorial form? Einstein summation convention was used here. Context: The above expression was derived from the derivation of torque on a general current distribution. It is part of an expression obtained by considering $$\left[\left(\vec{x}\times\vec{J}_1(\vec{x}')\right)\left(\vec{J}_2(\vec{x})\cdot\vec\nabla\frac{1}{|\vec x-\vec x'|}\right)\right]_k$$ My source of confusion is that I am suppose to obtain a divergence term from the first expression but there is the $x_m$ term in the square brackets. As such, I am unsure of how to proceed. [/QUOTE]
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Help with Levi-Civita manipulation
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