What is the ruling of Islamic law regarding a man having intercourse with his wife while she is fasting on the Day of Arafah, given that she had intended to fast before intercourse but completed her fast?

There is no blame on the questioner, and it is not permissible for a woman to observe a voluntary fast except with the permission of her present husband. There is no blame on her for not completing her fast, because a supererogatory fast is not obligatory, and it is not binding upon starting it according to some scholars. The wife's fast mentioned is invalid because sexual intercourse nullifies the fast by consensus.