B

Step 1: Understand the concept of equipotential surfaces. Equipotential surfaces are those surfaces where the potential is constant. For a point charge, the electric potential (V) at a distance r from the charge (Q) is given by the formula:
$$ V = \frac{kQ}{r} $$
where k is Coulomb's constant.

Step 2: Analyze the shape of the equipotential surfaces created by a point charge. Since the potential depends only on the distance from the charge, all points equidistant from the point charge have the same potential. Therefore, the surfaces of constant potential will be spherical in nature, with the charge located at the center of the sphere.

Step 3: Evaluate the options based on this reasoning.
- Option A (Ellipsoid with charge at foci): This does not apply because the potential is not constant along an ellipsoidal surface with a point charge.
- Option B (Sphere with charge at the center of the sphere): This is correct, as described.
- Option C (Sphere with charge on the surface of the sphere): This is incorrect because the point charge is at the center, not on the surface.
- Option D (Plane with charge on the surface): This is incorrect as paths of constant potential due to a point charge cannot be flat.

Therefore, the correct answer is B.