(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a vector field [itex]\vec{A}[/itex]([itex]\vec{r}[/itex]) in ℝ^{3}such that:

[itex]\vec{\nabla} \times \vec{A}[/itex] = y^{2}cos(y)e^{-y}[itex]\hat{i}[/itex] + xsin(x)e^{-x2}[itex]\hat{j}[/itex]

3. The attempt at a solution

I broke it down into a series of PDE's that would be the result of [itex]\vec{\nabla} \times \vec{A}[/itex]:

∂A_{3}/∂y - ∂A_{2}/∂z = y^{2}cos(y)e^{-y}

∂A_{3}/∂x - ∂A_{1}/∂z = -[-xsin(x)e^{-x2}] (since the j component has a negative sign)

∂A_{2}/∂x - ∂A_{1}/∂y = 0

By a little trial and error I came up with:

A_{1}= zxsin(x)e^{-x2}

A_{2}= -zy^{2}cos(y)e^{-y}

A_{3}= z

This can be verified that:

[itex]\vec{\nabla} \times \vec{A}[/itex] = y^{2}cos(y)e^{-y}[itex]\hat{i}[/itex] + xsin(x)e^{-x2}[itex]\hat{j}[/itex]

Is this a valid answer then?

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# Homework Help: Find Vector Field Given The Curl

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