What is the ruling on my sister traveling to study in a city 50 kilometers away and staying in a university dormitory specifically for girls, knowing that the study is mixed but the female students are isolated from the young men?

The basic principle is that there is no objection to a girl living outside her family home, provided she adheres to the

Shar'i hijab and its etiquette, and that the place is safe from mixing with non-mahram men and from any harm. As for a girl studying in a mixed-gender class, the mixing between genders in universities is forbidden and a cause for corruption. However, if a girl needs to study in a mixed-gender university, she must adhere to the controls of Sharia. If these conditions are met and the sister adheres to the controls, then there is no objection to her studying in the aforementioned university.