A current is set up in a wire loop consisting of a semicircle of radius $4\mathrm{.}23$ cm $,$ a smaller concentric semicircle, and two radial straight lengths, all in the same plane. Figure $($a$)$ shows the arrangement but is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature is $47\mathrm{.}28T.$ The smaller semicircle is then flipped over $($rotated$)$ until the loop is again entirely in the same plane $($Figure $($b$)).$ The magnetic field produced at the $($same$)$ center of curvature now has magnitude $15\mathrm{.}80T,$ and its direction is reversed. What is the radius of the smaller semicircle?

Number $$ Units