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Struggling with the following:

Prove the identity

$ \nabla = e_{r}(e_{r} \cdot \nabla) + e_{\theta}(e_{\theta} \cdot \nabla) + e_{\phi}(e_{\phi} \cdot \nabla).$

Given the vector fields $F=F_{r}e_{r}+F_{\theta}e_{\theta}+ F_{\phi}e_{\phi}$ show that

$ \nabla \cdot F=\frac{1}{r^{2}}\frac \partial {{\partial r}}(r^{2}F_r)+\frac{1}{r\sin\theta}\frac \partial {\partial \theta}(\sin\theta F_\theta)+\frac{1}{r\sin\theta}\frac \partial {\partial\phi} $

Any help will be most appreciated, many thanks.

  • 0
    @user16409: You ca$n$ flag it and ask the moderators to close it.2012-04-05

0 Answers 0