Answer
The electric field at the center of the sphere and outside the sphere is the same.
Work Step by Step
We kn ow that the electric field at the center of the sphere is given as:
$E=\frac{1}{4\pi \epsilon_{\circ}}\frac{q}{r^2}$.....eq(1)
Given that $E=\frac{\sigma}{\epsilon_{\circ}}$ where $\sigma$ is surface charge density and $\sigma=\frac{q}{A}$.
Thus,
$E=\frac{q}{A}\frac{1}{\epsilon_{\circ}}$
$\implies E=\frac{q}{4\pi r^2}\frac{1}{\epsilon_{\circ}}$ (as $A=4\pi r^2$)
This can be rearranged as:
$E=\frac{1}{4\pi \epsilon_{\circ}}\frac{q}{r^2}$........eq(2)
From eq(1) and eq(2), it is clear that electric field at the center of the sphere and outside the sphere is the same.
