I have school on Fridays, so I literally have to run to the Masjid (a few blocks away) after classes are over so I can make it in time for Jumu'ah. I get to the Masjid right when the Khutbah is about to be over, so I only get to listen to the last 5-10 minutes of the khutbah, or less. I cannot come to the Masjid to listen from the beginning because I have classes, and I barely make it in time for the 2 Fard, so its just not possible.
Is it wajib for me to listen to the full khutbah? Is my Jumu'ah salah still valid?