Consider two fields F₁ xi + yj and F₂ -yi xj and two curves: the circle r₁(t) = (cost)i + (sin t)j and the ellipse r₂(t) = (cost)i + (4 sint)j (0 ≤ t ≤ 2π).
Consider two fields F₁ xi + yj and F₂ -yi xj and two curves: the circle r₁(t) = (cost)i + (sin t)j and the ellipse r₂(t) = (cost)i + (4 sint)j (0 ≤ t ≤ 2π).
Consider two fields F₁ xi + yj and F₂ -yi xj and two curves: the circle r₁(t) = (cost)i + (sin t)j and the ellipse r₂(t) = (cost)i + (4 sint)j (0 ≤ t ≤ 2π).
a) Draw 4 pictures showing all possible combinations of a vector field and a curve
b) Compute the circulation and the flux
Transcribed Image Text:Consider two fields F₁
xi+yj and F₂
-yi xj and two curves: the circle
r₁(t) = (cost)i + (sin t)j and the ellipse r₂(t) = (cost)i + (4 sin t)j (0 ≤ t ≤ 2π).
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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