Answer: [tex]3.32\times 10^4\ kN/C[/tex]
Explanation:
Given
Charge at the center of the sphere is [tex]q=2\ nC[/tex]
Charge distributed over the entire sphere [tex]Q=1\ nC[/tex]
Radius of sphere [tex]r=4.8\ cm[/tex]
Using Guass law
[tex]\Rightarrow \oint \vec{E}\cdot \vec{dA}=\dfrac{q_{enc}}{\epsilon_o}\\\\\Rightarrow E\cdot 4\pi r^2=\dfrac{1}{\epsilon}(q+\dfrac{Q}{4\pi R^2}\times 4\pi r^2)\\\\\Rightarrow E\cdot 4\pi r^2=\dfrac{1}{\epsilon}(q+Q\dfrac{r^2}{R^2})\\\\\Rightarrow E\cdot (2.4\times 10^{-2})^2=9\times 10^9(2+1\cdot \dfrac{1}{4})\times 10^{-9}\\\\\Rightarrow E=3.32\times 10^4\ kN/C[/tex]
