# Coulomb gauge derivation (static field)

kidsasd987
Hi, I am a little confused of derivation of Coulomb Gauage.

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First, prime notation is adopted to describe the magnetic field density source current.
Non-prime notation is for position that we are specifically interested in (ex. the position magnetic force acts on).

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if equation (13) is true, then divergence of vector potential is 0.

Hence,
(13)
(14)

we can use vector indentity (14) to express (13) in another form.
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at this step, I am lost. We can break down divergence of vector potential into
two parts. I understand the first part is 0 because we assume that the field is static with respect to time,
but I wonder why the second flux integral part is 0.

(reference: http://ghebook.blogspot.ca/2011/06/energy-of-magnetic-field.html)

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$$\partial_t \rho + \vec{\nabla} \cdot \vec{J}=0,$$