To solve this problem we will use the concept of electric field, with which we will make the proportional comparison as we move away from the center. So we have the maximum electric field is given as,
[tex]E_{max} = \frac{kQ}{R^2}[/tex]
Where,
Q = Charge
R = Radius
Electric field inside the sphere is given as,
[tex]\frac{kQ}{R^2} = \frac{1}{2}\frac{kQ}{R^2}[/tex]
[tex]R'=\sqrt{2}R[/tex]
[tex]R' = 3\sqrt{2}[/tex]
[tex]R' = 4.2cm[/tex]
Electric field outside the sphere is given as,
[tex]\frac{kQ}{2R^2} = \frac{1}{2}\frac{kQ}{R^3}r[/tex]
[tex]\frac{1}{2} = \frac{r'}{R}[/tex]
[tex]\Rightarrow \frac{R}{2} = \frac{3}{2} = 1.5cm[/tex]
Therefore the possible values are 3.5cm and 9.9cm: The correct answer is D.
