Is it permissible for a married woman to complete her studies in the country of scholarship for the benefit of her country and to avert the risk of her remaining at home?

There is no sin upon you for continuing your studies with your husband in the country he will travel to. In fact, it is preferable, provided you are safe from temptation and adhere to Islamic guidelines, such as proper Islamic dress and avoiding mixing [with unrelated men]. However, if you are not safe from temptation, then it is not permissible for you to continue your studies. In that case, you can either remain in your country if it is safe, or your husband can forgo the trip, or you can choose not to accompany him.