A force field is described by #<F_x,F_y,F_z> = < x +y , 2z, 2y -z > #. Is this force field conservative?

Answer 1

The force field is not conservative bacause #vec grad xx vec F ne vec 0#

Finding the force field curl that we possess

The number ((hat i, hat j, hat k), (partial/(partial x), partial/(partial y), partial/(partial z)), (x+y,2z,2y-z)) = (0,0,-hat k)

which is different from #vec 0#

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Answer 2

Nora Arzate

To determine if the force field is conservative, check if the curl of the vector field is zero. If the curl is zero, the field is conservative. The curl of the given force field is zero, so it is conservative.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

A force field is described by #&lt;F_x,F_y,F_z&gt; = &lt; x +y , 2z, 2y -z &gt; #. Is this force field conservative?

A force field is described by #<F_x,F_y,F_z> = < x +y , 2z, 2y -z > #. Is this force field conservative?