Irodov Homework Help: Potential of Fields of Force

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To determine if the given fields of force are potential, one must check if the curl of the total fields is zero. The discussion highlights that calculating the work done by these forces can indicate whether the work is path-dependent, which is essential for identifying potential fields. The concept of path independence is crucial, as it implies that the work done is only dependent on the initial and final points. The mention of a "red card" suggests confusion or a warning about misunderstanding the topic. Ultimately, verifying the curl of the fields is emphasized as a reliable method for assessing their potential nature.
danilo_rj
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I've got a problem from Irodov.
There are two stationary fields of force F=ayi and F = axi + byj, where i and j are unit vectors of the x and y axes, and a and b are constants. Find out whether these fields are potential.
But how do I know that a field is potential? I've read that I have to calculate the work performed by these forces and if the work depends on the path or not. But why of this?
 
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what does this red card mean?
 
I think Checking whether the curl of total fields is zero or not is the best way
 

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