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

Explanation

To solve the problem of finding the electric field intensity in vector form at the specified positions around a solid non-conducting sphere of radius \( R \) and uniform volume density \( \rho \), we will follow these steps:

### Step 1: Understand the Electric Field Inside and Outside the Sphere

1. **Inside the Sphere** (for \( r < R \)):
The electric field \( \mathbf{E} \) at a distance \( r \) from the center of the sphere is given by:
\[
\mathbf{E} = \frac{\rho}{3 \epsilon_0} \mathbf{r}
...