To solve this problem, we need to find the magnetic field produced at the center of a circular orbit by an electron moving in that orbit.$\\$Given:$\\$• Radius of the orbit $r \\$• Number of rotations per second $n \\$The magnetic field at the center of a circular loop carrying current $I$ is given by:$\\ B = \frac{\mu_0 I}{2r} \\$Here, $\mu_0$ is the permeability of free space.$\\$To find the current $I,$ we consider the charge moving in the loop.$\\$The charge of an electron is $e. \\$The current $I$ is defined as charge per unit time. Since the electron makes $n$ rotations per second,$\\ I =$charge per rotation$\times$rotations per second$\\ I = e \times n \\$Substitute $I = en$ into the magnetic field equation:$\\ B = \frac{\mu_0 (en)}{2r} \\$Therefore, the magnetic field produced at the center is:$\\ B = \frac{\mu_0 ne}{2r} \\$This corresponds to Option 3.