Two choices
Target the spell, which should take down the entire spell. However, given how effects outside a spell's range do not happen, you as DM do have the power to say only the area within the range of the caster's dispel magic spell is dispelled. The Magic item will recast te spell the following evening.
Area dispel will carve out the 20' radius. The Magic item will recast te spell the following evening.
Range
A spell’s range indicates how far from you it can reach, as defined in the Range entry of the spell description. A spell’s range is the maximum distance from you that the spell’s effect can occur, as well as the maximum distance at which you can designate the spell’s point of origin. If any portion of the spell’s area would extend beyond this range, that area is wasted.
Targeted Dispel
One object, creature, or spell is the target of the dispel magic spell. You make a dispel check (1d20 + your caster level, maximum +10) against the spell or against each ongoing spell currently in effect on the object or creature. The DC for this dispel check is 11 + the spell’s caster level. If you succeed on a particular check, that spell is dispelled; if you fail, that spell remains in effect.
If you target an object or creature that is the effect of an ongoing spell (such as a monster summoned by monster summoning), you make a dispel check to end the spell that conjured the object or creature.
If the object that you target is a magic item, you make a dispel check against the item’s caster level. If you succeed, all the item’s magical properties are suppressed for 1d4 rounds, after which the item recovers on its own. A suppressed item becomes nonmagical for the duration of the effect. An interdimensional interface (such as a bag of holding) is temporarily closed. A magic item’s physical properties are unchanged: A suppressed magic sword is still a sword (a masterwork sword, in fact). Artifacts and deities are unaffected by mortal magic such as this.
You automatically succeed on your dispel check against any spell that you cast yourself.
Area Dispel
When dispel magic is used in this way, the spell affects everything within a 20-foot radius.
For each creature within the area that is the subject of one or more spells, you make a dispel check against the spell with the highest caster level. If that check fails, you make dispel checks against progressively weaker spells until you dispel one spell (which discharges the dispel magic spell so far as that target is concerned) or until you fail all your checks. The creature’s magic items are not affected.
For each object within the area that is the target of one or more spells, you make dispel checks as with creatures. Magic items are not affected by an area dispel.
For each ongoing area or effect spell whose point of origin is within the area of the dispel magic spell, you can make a dispel check to dispel the spell.
For each ongoing spell whose area overlaps that of the dispel magic spell, you can make a dispel check to end the effect, but only within the overlapping area.
If an object or creature that is the effect of an ongoing spell (such as a monster summoned by monster summoning) is in the area, you can make a dispel check to end the spell that conjured that object or creature (returning it whence it came) in addition to attempting to dispel spells targeting the creature or object.
You may choose to automatically succeed on dispel checks against any spell that you have cast.
