Is it permissible for a woman to work as a doctor in mixed-gender hospitals if her husband's salary is insufficient to cover essential expenses and the family is forced to incur debt?

A woman working as a doctor is permissible, provided she observes the Islamic legal guidelines. These include not treating men unless there is a necessity or a need deemed valid by Islamic law, especially concerning the exposure of awrah (private parts). The financial support of the wife and children is obligatory upon the husband to suffice their needs. If the husband fails to provide sufficiently, and the wife is compelled to work as a doctor and finds no means except in mixed-gender hospitals, there is no sin upon her, provided she fears Allah. However, she must leave this work once she is no longer in need of it, as necessity is judged according to its extent.