According to Faraday's Law of Induction, the induced emf is given by $\varepsilon = -\frac{d\Phi_B}{dt}$ .

1. Loop 1: This loop (Radius $R$) encloses the cylindrical region of the magnetic field (Radius $r$). Since the field $B$ exists only within radius $r$, the total magnetic flux through Loop 1 is determined by the area of the magnetic field region, not the area of the loop itself. Flux $\Phi_1 = B \times (\text{Area of field}) = B(\pi r^2)$. Induced emf $\varepsilon_1 = -\frac{d}{dt}(B\pi r^2) = -\pi r^2 \frac{dB}{dt}$.

2. Loop 2: This loop is situated entirely outside the region of the magnetic field. Therefore, no magnetic field lines pass through it. Flux $\Phi_2 = 0$. Induced emf $\varepsilon_2 = -\frac{d(0)}{dt} = 0$.

Thus, a non-zero emf depends on the rate of change of field and the area of the field enclosed, while a loop enclosing no flux generates zero emf.