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The vector function $F\left ( r \right )=-x\hat{i}+y\hat{j}$ is defined over a circular arc $C$ shown in the figure.

The line integral of $\int _{C} F\left ( r \right ).dr$ is

  1. $\frac{1}{2}$
  2. $\frac{1}{4}$
  3. $\frac{1}{6}$
  4. $\frac{1}{3}$
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