Mention the three states by which matter exists.

Step 1: The magnitude of the induced emf $\mathcal{E}$ in the $N$-turn coil is given by Faraday's law, where the magnetic flux changes due to the area leaving the field:

$\mathcal{E} = N B l v$

Here, $N = 100$ (dimensionless turns), $B = 0.2$ T (tesla), $l = 10$ cm $= 0.10$ m (length of side perpendicular to $\vec{v}$), $v = 0.5$ m/s (speed).

Step 2: Substitute the values into the formula:

$\mathcal{E} = 100 \times 0.2 \, T \times 0.10 \, m \times 0.5 \, \mathrm{m/s}$

Step 3: Simplify step-by-step:

$0.2 \times 0.10 = 0.02 \, \mathrm{T \cdot m}$

$0.02 \times 0.5 = 0.01 \, \mathrm{T \cdot m^2/s}$

$100 \times 0.01 = 1 \, \mathrm{V}$

So, the induced emf is $\mathcal{E} = 1$ V.

Step 4: The magnitude of the induced current $I$ in the loop is given by Ohm's law:

$I = \frac{\mathcal{E}}{R}$

Here, $R = 0.1 \, \Omega$ (ohms).

Step 5: Substitute the values:

$I = \frac{1 \, V}{0.1 \, \Omega}$

Step 6: Simplify:

$I = 10 \, \mathrm{A}$

Induced emf $= \boxed{1 V}$, induced current $= \boxed{10 A}$.