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My notes say that if we know the divergence and curl of a field then that uniquely determines the field.

Can somebody give me an example of how, given only the div and curl of a field, we can deduce the field?

I considered the electric field where we have,

[itex]\nabla \cdot \vec{E}=\frac{\rho}{\epsilon_0}, \nabla \times \vec{E}=0[/itex]

but we can't actually establish E using only vector calculus can we? we need other techniques do we not? perhaps i'm just being silly?

Can somebody give me an example of how, given only the div and curl of a field, we can deduce the field?

I considered the electric field where we have,

[itex]\nabla \cdot \vec{E}=\frac{\rho}{\epsilon_0}, \nabla \times \vec{E}=0[/itex]

but we can't actually establish E using only vector calculus can we? we need other techniques do we not? perhaps i'm just being silly?

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