# I What is the gradient of a divergence and is it always zero?

#### James Essig

Hi Folks,

Was just curious as to what is the gradient of a divergence is and is it always equal to the zero vector. I am doing some free lance research and find that I need to refresh my knowledge of vector calculus a bit. I am having some difficulty with finding web-based sources for the gradient of a divergence.

#### James Essig

Thanks for the info fresh_42. I found those two links very helpful and I solved my problem of the reason for my inquiry.

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One very important vector identity, (it is used in showing Maxwell's equations result in an electromagnetic wave equation), is $\nabla \times \nabla \times \vec{A}=\nabla (\nabla \cdot \vec{A})-\nabla^2 \vec{A}$. For the case that is often shown to demonstrate the wave equation in a vacuum, $\nabla \cdot \vec{E}=0$, but in general, the first term on the right side of the vector identity equation is not equal to zero.