Smartbombs are activated from your ship and radiate outwards in a ring. They will not damage your ship but will damage anything else friendly or foe withing their radius. Be very careful playing with smartbombs in Highsec(.5 and higher) because if you hit anybody that that is not a legal target concord will show up and quickly relieve you of your ship by way of wtfbbqpwnage.

If by chance you are mistaken and are thinking of a bomb that is launched from a Stealthbomber then yes if you are in the blast zone when it explodes you will take damage and may even blow yourself up.