A flat circular coil with 184 turns, a radius of $3.44 \times 10^{-2}$ m, and a resistance of $0.237 \, \Omega$ is exposed to an external magnetic field that is directed perpendicular to the plane of the coil. The magnitude of the external magnetic field is changing at a rate of $\frac{\Delta B}{\Delta t} = 0.854 \, T/s$, thereby inducing a current in the coil. Find the magnitude of the magnetic field at the center of the coil that is produced by the induced current.