A non-conducting solid sphere has radius \(R\) and uniform charge density. A spherical cavity of radius \(\frac{R}{4}\) is hollowed out of the sphere. The distance between center of sphere and center of cavity is \(\frac{R}{2}\). If the charge of the sphere is \(Q\) after the creation of the cavity and the magnitude of electric field at the center of the cavity is \(E=K\left(\frac{Q}{4 \pi \in_0 R^2}\right)\), determined the approximate value of \(K\).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.