About 70,000 km. If the Earth orbited Jupiter (or flew by) at a closer distance, not just we would leave the surface, but the whole Earth would disintegrate since all its mass will be leaving too.
70,000 km is Jupiter's Roche limit (although its actual value varies a lot depending on the other involved body), the radius where tidal forces (already explained in uhoh's answer) overwhelm gravitational forces and any orbiting body cancan't hold itself by its own weight. In that context, people on the surface don't behave differently than rocks.
Btw., this scenario is also explored in a youtube video. I wouldn't say it's very good but it may be helpful to explain the Roche limit to a 7 year old.