Last Update Date and Time

I have a simple timesheet excel sheet where I keep track of all my TO DO activities. I have a columm called Start Date to keep track of when I started something. Rather than filling it up manually, I came up with the formula below and thought I was a genius.
=IF(B2<>"",NOW(),"")

But, now as luck would have it, all my rows get updated every time I save the worksheet.

My requirement is very simple. I need to track when content was added to a cell. (even a NULL check is fine). As soon as content is added to column A, the date/time should appear automatically in column B and stay there forever.

Plz help!