The maximum induced electromotive force ($\varepsilon_{max}$) in a rotating coil is given by the formula $\varepsilon_{max} = NBA\omega$, where: $N$ is the number of turns ($1000$). $B$ is the magnetic field ($2 \times 10^{-5} \text{ T}$). $A$ is the area of the coil ($\pi r^2 = \pi (10)^2 = 100\pi \text{ m}^2$). $\omega$ is the angular velocity ($2 \text{ rad s}^{-1}$).

The maximum induced current ($I_{max}$) is given by Ohm's law: $I_{max} = \frac{\varepsilon_{max}}{R}$.

Substituting the values: $I_{max} = \frac{1000 \times (2 \times 10^{-5}) \times (100\pi) \times 2}{12.56}$

Noting that $12.56 \approx 4\pi$: $I_{max} = \frac{1000 \times 2 \times 10^{-5} \times 100\pi \times 2}{4\pi}$ $I_{max} = \frac{400000 \pi \times 10^{-5}}{4\pi}$ $I_{max} = \frac{4\pi}{4\pi} = 1 \text{ A}$.