Is zakat obligatory on the dowry amount paid to the wife, which was designated for purchasing household furniture, if a year has passed and it has reached the nisab?

The woman's mahr (dowry) is subject to the same ruling as the rest of her wealth concerning zakat. If a full year passes while it is in her possession, and it reaches the nisab (minimum threshold) either by itself or when combined with other wealth of the same type she owns, then zakat becomes obligatory on it. The fact that it is earmarked for purchasing household necessities does not exempt it from this ruling, unless the purchases are made before the completion of the year, because furniture and possessions are not subject to zakat.