Bisecting with a curve

I understand that I can bisect a model using the bisect tool, but it appears to only work in a straight line. Is there a clean and simple way to bisect an object using a custom made plane as the bisect line? In the file I attached, I would like to bisect the sphere along the curve.
Thanks in advance…

Attachments

Bisected Sphere Exercise.blend (541 KB)

not with the bisect tool, but you could use the curve plane as a knife with the knife project tool or the boolean modifier

1)Boolean: Duplicate sphere, make booleans with plane object, one difference, one intersect and you have top part and bottom part.
2)Knife project: Profile plane without faces and cut through. Rip(V) connecting edges.

Attachments