This paper presents an adaptive path planner for object search in agricultural fields using UAVs. The path planner uses a high-altitude coverage flight path and plans additional low-altitude inspections when the detection network is uncertain. The path planner was evaluated in an offline simulation environment containing real-world images. We trained a YOLOv8 detection network to detect artificial plants placed in grass fields to showcase the potential of our path planner. We evaluated the effect of different detection certainty measures, optimized the path planning parameters, investigated the effects of localization errors, and different numbers of objects in the field. The YOLOv8 detection confidence worked best to differentiate between true and false positive detections and was therefore used in the adaptive planner. The optimal parameters of the path planner depended on the distribution of objects in the field. When the objects were uniformly distributed, more low-altitude inspections were needed compared to a non-uniform distribution of objects, resulting in a longer path length. The adaptive planner proved to be robust against localization uncertainty. When increasing the number of objects, the flight path length increased, especially when the objects were uniformly distributed. When the objects were non-uniformly distributed, the adaptive path planner yielded a shorter path than a low-altitude coverage path, even with a high number of objects. Overall, the presented adaptive path planner allowed finding non-uniformly distributed objects in a field faster than a coverage path planner and resulted in a compatible detection accuracy. The path planner is made available at https://github.com/wur-abe/uav_adaptive_planner.