Question

Exercise. Below we have plotted a discrete "sampling of a vector field: -2 2 4 Let C be a circle of radins 3 centered at the origin drawn in a counterclockwise fashion. What concusions seem to be true? This is a gradieut field This is not a gradient field. This field has positive cur This field bas negative curl. c F.dp X Try again Note that the raclias of the circle is irreverent.

Answer 1

Hey there!

If a circle has the path in the counterclockwise direction. And when the circle is drawn we could see that the field is perpendicular to each point of the circle. In that sense it means , the function is increasing in the fastest way possible. Hence this field is a gradient field. Also since the path is a close contour , we could say that

F.dp = 0
  

in the contour.

If the field was rotating in the couterclockwise direction it would have been a positive curl. But in our case, the field is a gradient and not a curl.

I hope the solution helps. Cheers :)