1. Given data

• Number of turns: $N = 200$
• Area of coil: $A = 0.20\,\text{m}^2$
• Magnetic field: $B = 0.01\,\text{T}$
• Rotational frequency: $f = \dfrac{1}{2}\,\text{rev/s}$

Since the magnetic field is perpendicular to the axis of rotation, the flux through the coil changes sinusoidally, so the induced emf is

$e = N B A \omega \sin(\omega t)$

Hence the maximum emf is

$E_{\max} = N B A \omega$

2. Find angular speed

$\omega = 2\pi f = 2\pi \left(\frac{1}{2}\right) = \pi\,\text{rad/s}$

3. Compute maximum emf

$E_{\max} = N B A \omega$

Substitute the values:

$E_{\max} = 200 \times 0.01 \times 0.20 \times \pi$

Now,

$200 \times 0.01 = 2$

$2 \times 0.20 = 0.4$

So,

$E_{\max} = 0.4\pi = \frac{2\pi}{5}\,\text{V}$

4. Compare with given form

Given,

$E_{\max} = \frac{2\pi}{\beta}$

Thus,

$\frac{2\pi}{\beta} = \frac{2\pi}{5}$

So,

$\beta = 5$

5. Comparison with stored answer

Stored correct answer = $5$

Our derived answer also gives $\beta = 5$.