は vs.では in こんなうるさいところでは勉強ができません

Question

こんなうるさいところでは勉強ができません。

How is the meaning of the sentence above different from the meaning of the one below?

こんなうるさいところで勉強ができません。

Answer 1

は in a negative sentence can indicate the scope of negation. Compare:

こんなうるさいところでは勉強ができません。
こんなうるさいところで勉強はできません。

Both can be used almost interchangeably in most situations, but the former can imply "I can't study in such a noisy place (but I could study in other places)." while the latter "I can't study in such a noisy place (but I could do other things here)." (i.e. in the former, こんなうるさいところで part is negated, and in the latter, 勉強(できる) is negated.)

(こんなうるさいところで勉強ができません doesn't sound natural)