# consevative field hep

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• Jul 18th 2013, 04:14 PM
n22
consevative field hep
Hello, please help.cheers
Let G =2xyzi+(x^2z+2y)j+(x^2y-2z)k

calculate ∇xG and show that G is conservative field Find the work done by G:
around the closed curve x²+y²=1 in the plane z=0, transversed in a counterclockwise direction,starting and ending at the point (1,0,0).

• Jul 18th 2013, 04:28 PM
HallsofIvy
Re: consevative field hep
Okay, have you not tried this yourself? The standard calculation for $\nabla\times G$ is $\left|\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ 2xyz & x^2z+2y & x^2y- 2z \end{array}\right|$. You knew that didn't you? The result is is very simple as you should suspect because the next part is "show that G is a conservative field". What must be true of $\nabla\times G$ in order that the field be conservative? And what is true about the work done in moving an object around a closed path in a conservative force field?