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**V**(x, y, z) in three dimensional space, is it possible to create an electric field that is described by

**V**.

Someone told me that according to Helmholtz theorem, a vector field (with certain constrains) can be expressed as a sum of a curless field and a divergenceless field. To me since charge density is basically the divergence of the electric field, and change in B field creates curl in electric field, it should be possible to create any electric field with these two elements. The procedure would be: given

**V**, decompose it into a curless field and a divergenceless field; then put electric charges in space such that the charge density is described by the divergenceless field at all points; similary, do the same with ∂B/∂t at each point to create curl in E field that is described by the curless field; since E field obeys the superposition principle, everything should add and the resulting E field would be

**V**.

Now the thing is I'm not familiar with Helmholtz theorem and the conditions it requires. Can someone clarify?