What is this faint ringing in my ear?

Your ears are reacting to different pressures when you fly or dive deep into water. The air pressure changes at different altitudes and your ears react to this change. The ringing is called tinnitus and can happen also when the pressure changes for some reason. I'm not so sure why you should be getting this when your just doing home work but try chewing some gum and see if it helps. Use sugar free so it won't damage your teeth. I would also see your doctor asap as it may have something to do with some type of damage that might have happened when you were younger and went into a plane with an ear infection. It definitely would not hurt to get them checked to be sure. Good luck and God Bless