Conservative field problems, screencap of problems posted below, working on them right now.

Question

mendicant_bias · Answer

mendicant_bias · Answer

Alright, working on 1 first:

anonymous · Answer

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anonymous · Answer

please??

anonymous · Answer

Conservative means it has a potential function $f$ such that: $$
\nabla f = \mathbf F
$$Right?

mendicant_bias · Answer

Yeah, I just forgot how to do this mechanically, it has to do with partial derivatives, lol.

anonymous · Answer

I believe that having a curl of 0 implies that it is conservative.

anonymous · Answer

So $$
\nabla \times \mathbf F = 0
$$

mendicant_bias · Answer

Alright, cool. So I just have to take the curl of each of these to show whether it is or is not conservative, can do. One second.

mendicant_bias · Answer

mendicant_bias · Answer

Alright, I understand how to do that, going to move on to a different type of problem,  finding the potential function for a given vector field.

anonymous · Answer

New problem means new question.

mendicant_bias · Answer

Yup, opened up a new question.