Say a wizard casts a delayed blast fireball and leaves it to charge up instead of detonating it immediately. Another wizard casts antimagic field and moves so that the fireball bead is inside of the AMF. Now what happens if the first wizard ends concentration to detonate the fireball?

Obviously anyone inside of the AMF won't be affected, but what about creatures outside of it, but within the blast radius of the fireball? Are they unaffected because the fireball bead is inside of the AMF and thus can't detonate, or are they affected because only the area inside the AMF is blocking magic?

A Delayed Fireball in an Antimagic Field wouldn't detonate

The Antimagic Field(AMF) nullifies the magic contained within the Delayed Blast Fireball(DBF) bead, making it unable to do anything while in the AMF.

From Antimagic Field:

Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the sphere and can't protrude into it. ... While an effect is suppressed, it doesn't function, but the time it spends suppressed counts against its duration.

If the DBF's caster ends their concentration while the bead is in the AMF, the effect is suppressed, meaning nothing happens. The spell description says: "the bead blossoms with a low roar into an explosion of flame", and the bead can't do that while suppressed. If the AMF moves over the DBF bead and then moves out before the DBF's duration expires, then any turns spent holding the spell still count for increased damage as normal.