Instead of taking the whole system into your hands (that, granted, it can be done and I have done it in the past) you may want to take a look at log4net.
You can break your categories to INFO,WARNING,ERROR etc and you can choose a size that after reached it will create a new file.
I'm writing this as from what I understand, this is not for educational purposes but for a real app, so that's a more secure way of logging data.

P.S. Credit to JMC as a few years back reminded me of this solution.