Final answer:
The correct answer is A. The expression for the electric field of a uniformly charged non-conducting sphere depends on the distance from the center of the sphere, which changes within and outside the sphere.
Step-by-step explanation:
The student's question relates to the electric field of a uniformly charged non-conducting sphere, which can be answered using concepts from Gauss's Law in electrostatics.
Inside a non-conducting sphere with uniform charge density, the electric field varies with distance r from the center of the sphere according to E = (kq/r^3)r, where k is Coulomb's constant, q is the total charge, and r is the distance from the center. Outside the sphere, the electric field acts as if all the charge were concentrated at the center according to E = kq/r^2.
Thus, none of the provided options a. E = kq/r^2, b. E = kq/r, c. E = qr/k, d. E = kr/q precisely describe the electric field at all points both inside and outside the sphere. The correct formula is dependent on the position relative to the sphere's radius.