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Smazmbazm
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Homework Statement
Consider the vector field given by
[itex]F(x, y, z) = yz \hat{i} + xz \hat{j} + (xy + 3z^{2})\hat{k}[/itex]
a. Calculate ∇xF and show that F is a conservative field. Done, result = <0,0,0> which implies the vector field is conservative.
b. The way we were taught this is to set
[itex]
∂\phi /∂x = yz, \\
∂\phi /∂y = xz, \\
∂\phi /∂z = xy + 3z^{2}
[/itex]
Then find the integrals of all 3 equations to get,
[itex]
\phi = xyz + C_{x},\\
\phi = xyz + C_{y},\\
\phi = xyz + z^{3} + C{z}
[/itex]
Finally, look for similar features and construct [itex]\phi[/itex] like so
[itex]\phi = xyz + x^{3} + C[/itex]
Is that correct?
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