A graph of the induced EMF versus time for a coil rotating in a...

From the described graph, the peak-to-peak EMF is $628 \text{ V}$. The peak (maximum) induced EMF is half of this value:
E_\max = \dfrac{628}{2} = 314 \text{ V}

The time period $T = 0.02 \text{ s}$. The angular velocity $\omega$ is:
$\omega = \dfrac{2\pi}{T} = \dfrac{2 \times 3.14}{0.02} = 314 \text{ rad s}^{-1}$

The maximum induced EMF for a rotating coil is given by:
E_\max = NAB\omega

Substituting the given values ($N = 500$, $A = 0.1 \text{ m}^2$):
$314 = 500 \times 0.1 \times B \times 314$
$1 = 50 \times B$
$B = \dfrac{1}{50} = 0.02 \text{ T}$

Using the peak-to-peak value directly instead of the peak value leads to $0.04 \text{ T}$, while confusing angular velocity with frequency leads to $0.1256 \text{ T}$.

Answer: $0.02 \text{ T}$