\begin{align*}
\mathcal{E} &= N\frac{\Delta\phi}{\Delta t} \\
& = N\frac{\phi_{f} - \phi_{i}}{\Delta t} \\
& = N\frac{B_{f}A\cos \theta - B_{i}A \cos \theta}{\Delta t} \\
& = N\frac{A\cos \theta(B_{f} - B_{i})}{\Delta t} \\
& = 13 \left( \frac{\pi(\text{6,8} \times \text{10}^{-\text{2}})^{2}
\cos (\text{88})(\text{1,8} - (-\text{5}))}{18} \right) \\
& = \text{0,00249}\text{ V}
\end{align*}

If the angle is changed to \(\text{39}\)\(\text{°}\), what would
the radius need to be for the emf to remain the same?

\begin{align*}
\mathcal{E} &= N\frac{\Delta\phi}{\Delta t} \\
& = N\frac{\phi_{f} - \phi_{i}}{\Delta t} \\
& = N\frac{B_{f}A\cos \theta - B_{i}A \cos \theta}{\Delta t} \\
& = N\frac{A\cos \theta(B_{f} - B_{i})}{\Delta t} \\
\text{0,00249}& = 13 \left( \frac{\pi(r)^{2} \cos
(\text{39})(\text{1,8} - (-\text{5}))}{18} \right) \\
\text{0,04482}& = \text{215,83}(r)^{2} \\
r^{2} & = \text{0,00002077}\\
r & = \text{0,014}\text{ m}
\end{align*}