Answer
See the detailed answer below.
Work Step by Step
We can see that when the patient moves his eye the orientation of the coil changes. This makes the angle between the magnetic field vector and the area vector of the coil change from 90$^\circ$ to 85$^\circ$.
So the induced emf is given by Faraday’s law,
$$\varepsilon_{\rm coil}=N\left| \dfrac{d\Phi}{dt}\right|$$
where $ \Phi =\vec A\cdot \vec B =AB\cos\theta $ where $A$ and $B$ are constants, so
$$\varepsilon_{\rm coil}=NAB\left| \dfrac{d\cos\theta}{dt}\right|$$
$$\varepsilon_{\rm coil}=\pi r^2N B\left| \dfrac{ \cos\theta_f-\cos\theta_i}{dt}\right|$$
Plug the known;
$$\varepsilon_{\rm coil}=\pi(3\times 10^{-3})^2(20)(1)\left| \dfrac{ \cos85^\circ-\cos90^\circ}{0.20}\right|$$
$$\varepsilon_{\rm coil}=\color{red}{\bf 2.46\times 10^{-4}}\;\rm V$$
