Consider a sphere of radius $$R$$ which carries a uniform charge density $$\rho$$. If a sphere of radius $$\frac{R}{2}$$ is carved out of it, as shown, the ratio $$\frac{|\vec{E_A}|}{|\vec{E_B}|}$$ of magnitude of electric field $$\vec{E_A}$$ and $$\vec{E_B}$$, respectively, at points $$A$$ and $$B$$ due to the remaining portion is:

A

$$\frac{21}{34}$$

B

$$\frac{18}{34}$$

C

$$\frac{17}{54}$$

D

$$\frac{18}{54}$$