So far you are on the right track... Just think about where the charge is in relation to your Gaussian Surface. It's very important that you understand this!
Applying Newton's Second Law:
m\ddot{y}=FT-mg
g here is just +9.8. The "downward" direction of gravity is already taken care of by the minus sign in :
FT-mg
Rewriting it as
FT=m(\ddot{y}+g)
Just plug and chug...
You should get a positive tension force
Hmm...How do I way this? Force and field are related concepts but not entirely the same thing.
First of all you would be right to say that the field in some space would be altered if you introduce a test charge or any charge for that matter into the "picture" and if I throw in another charge...