What is the Sharia ruling regarding a woman's work (electronics maintenance) where she goes out with her face uncovered and speaks to men because of work, given that her husband refuses for her to wear the niqab or stay at home, and she feels that she is committing sins, knowing that she is not adorned, is elderly, a mother of four children, does not own a home, and refuses usurious loans?

A woman's work that involves being alone with non-mahram men or mingling in a way that does not ensure protection from fitna (temptation/strife) is impermissible. If the woman is in need of work, and interaction with men is limited and controlled by the regulations of Sharia, and restricted to the extent of necessity, then it is permissible. The husband is not obliged to force his wife to work, because the household expenses are his responsibility. If a woman works in a permissible occupation and helps her husband, that is an act of ihsan (benevolence). If the woman follows the opinion that obliges covering the face, then she is not permitted to obey her husband in uncovering it, because obedience is only in what is good (ma'ruf). She can discuss with her husband kindly and remind him of the virtues of covering the face.