Is it permissible for a veiled female doctor to pursue a master's degree and specialize in a clinic for women, while acknowledging the possibility of examining men during her studies and examinations, with the aim of protecting Muslim women and preventing them from having to be examined by men?

A woman is permitted to study medicine if there is a need or necessity for it, while observing the fear of God as much as possible. Necessities permit the forbidden, and need may be considered as such. If a woman is sincere in her intention and intends to benefit Muslim women, she will be rewarded for it, as the Prophet, peace and blessings be upon him, said: "Actions are by intentions, and every person will have what they intended."