The figure shows a vector field F and two curves C1 and C2. Are the line integrals of F over C1, and C2 positive, negative, or zero? Explain.
Whether the expression is positive, negative, or zero.
Refer to Figure in the textbook (i.e., bottom of the question 16.2-18E).
Consider the curve in the quadrants II and III as curve and the curve in the first quadrant as curve .
The curve is the semi-circle which starts at the positive y-axis and ends at the negative y-axis.
Write the expression for a curve .
is the unit tangent vector.
The field vectors are started on the curve and most of the field vectors in the same direction as the curve .
As the direction of curve is same as the direction of path of the vectors of , the integration of is always positive
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