A higher voltage DIY generator?

The peak voltage generated by this little device is given by:

V = A x M x N

Where A is the cross sectional area of the can (0.0008 m²), M is the rate of change of magnetic field (ca. we need to use very strong magnets having a surface field of say 1 Tesla (see magnet info. below), so shaking it say 5 times a sec we get M = 5 Tesla / sec) and N the number of turns.
If we want an LED to light brightly we need to generate peak voltages of about 4V;

rearanging the formula allows us to estimate the number of turns:

N = V / (A x M) = 4 / (0.0008 x 5) = about 1000 turns - happy winding !

I am trying to create a DIY linear generator like http://www.creative-science.org.uk/gensimple1.html. However, I am wondering if this design I thought of will work or not or give more voltage or not.

Basically, instead of a solid coin-like NIB magnet like the one in the website, I will be using a hollow tube shape NIB magnet instead (please refer to image http://www.filefactory.com/file/ah2f2f4/n/Scan10085_JPG ).