Answer
About 4000 turns, but answers will vary.
Work Step by Step
Let the coil have a radius of 2.0 cm so the flashlight fits nicely in the user’s hand. As the magnet passes through the coil, the field in the coil changes direction. The change in flux for each pass is therefore twice the maximum flux.
Assume that the user shakes flashlight three times per second, so the magnet passes through the coil six times per second, and $\Delta t = \frac{1}{6}s$. Calculate the number of turns in the coil using equation 21–2b.
$$N=\frac{\epsilon}{\Delta \Phi/\Delta t}=\frac{\epsilon \Delta t }{\Delta \Phi }$$
$$N=\frac{(3V)(0.167s)}{2(0.05T)\pi(0.02m)^2 }\approx 4\times10^3$$
The answer will depend on the approximations that are made. For example, a smaller diameter flashlight will need more turns of wire.