Let C be a counter-clockwise planar circle with center at the origin and positiv

Question

Let C be a counter-clockwise planar circle with center at the origin and positive radius. Without computing them, determine for the following vector fields F whether the line integrals integral_C Fmiddot dr are positive, negative, or zero and type P, N, or Z as appropriate the radial vector field = F(x, y) = xi + yj:____________ the circulating vector field = F(x, y) = -yi + xj: _____________ the circulating vector field F(x, y) = yi- xj:__________ the constant vector field F(x, y) = i + j:______________

Explanation / Answer

A) The radial vector field is zero

B) the circulating vector field is positive

C) the circulating vector field is Negative

D) the constant vector field is zero

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