Is it permissible for a man to have intercourse with his wife after Fajr prayer and then leave for work without performing ghusl, intending to perform ghusl before Dhuhr prayer at his workplace, and is it obligatory for him to perform ghusl before leaving the house?

If a man performs ghusl for janabah before the Dhuhr adhan, there is no harm in it. However, it is preferable for him to hasten his ghusl so that no impediment at his workplace prevents him, and so that he remains in a state of purity, as the Prophet, peace and blessings be upon him, said: "And know that the best of your deeds is prayer, and none maintains ablution except a believer."