Let a, b be positive real numbers such that a < b. Given that \(\lim _{N \rightarrow \infty} \int_{0}^{N} e^{-t^{2}} d t=\frac{\sqrt{\pi}}{2}\) the value of \(\lim _{N \rightarrow \infty} \int_{0}^{N} \frac{1}{t^{2}}\left(e^{-a t^{2}}-e^{-b t^{2}}\right) d t\) is equal to