A solid non conducting sphere of radius R and uniform volume charge density `rho` has its centre at origin. Find out electric field intensity in vector form at following positions :
(i) `(R//2, 0, 0)" "`(ii) `(R/sqrt(2), R/sqrt(2), 0)" "`(iii) `(R, R, 0)`

Explanation

To find the electric field intensity at the specified points for a solid non-conducting sphere of radius \( R \) and uniform volume charge density \( \rho \), we will use the following principles:

1. **Electric Field Inside the Sphere**: For points inside the sphere (where \( r < R \)), the electric field \( \mathbf{E}_{\text{inside}} \) is given by:
\[ \mathbf{E}_{\text{inside}} = \frac{\rho r}{3 \epsilon_0} \hat{r} \]
where \( \hat{r} \) is the unit vector in the direction of the radius vector.

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