(Solved): The figure shows two parallel loops with a common axis. The smaller loop (radius \( r \) ) is abov ...

The figure shows two parallel loops with a common axis. The smaller loop (radius \( r \) ) is above the larger loop (radius \( R \) ) at a distance \( X>>R \). As a result, the magnetic field produced by a current i passing through the larger loop in a counterclockwise direction is practically uniform in the region bounded by the smaller loop. Distance \( \mathrm{X} \) is increasing at a constant rate \( \mathrm{dx} / \mathrm{dt}=\mathrm{V} \). Indicate the alternative that best represents the electromotive force \( \epsilon \) through the smaller coil as a function of \( x \). a. \( \epsilon=\frac{3 \mu_{0} i r^{2} R^{2}}{2 \pi x^{3}} \) b. \( \epsilon=\frac{3 i r^{2}}{2 \pi R^{2} \mu_{0} x^{4}} \) c. \( \epsilon=\frac{3 \pi \mu_{0} i r R^{2}}{2 x^{3}} \) d. \( \epsilon=\frac{3 i r^{2} R^{2}}{2 \pi \mu_{0} x^{3}} \) e. \( \epsilon=\frac{3 \pi \mu_{0} i i^{2} R^{2} v}{2 x^{4}} \)