Figure $($a$)$ shows two wires, each carrying a current. Wire $1$ consists of a circular arc of radius $R=0\mathrm{.}023m$ and two radial lengths; it carries current $i_1=2\mathrm{.}1A$ in the direction indicated. Wire $2$ is long and straight; it carries a current $i_2$ that can be varied; and it is at distance $\frac{R}{2}$ from the center of the arc. The net magnetic field vec$(B)$ due to the two currents is measured at the center of curvature of the arc. Figure $($b$)$ is a plot of the component of vec$(B)$ in the direction perpendicular to the figure as a function of current $i_2.$ The horizontal scale is set by $i_{2s}=1\mathrm{.}0A.$ What is the angle subtended by the arc?

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