There is a solid non-conducting sphere of radius R. Sphere is uniformly charged over the volume. Electric field due to this where in observed.

Options

A. Electric field intensity at the centre of sphere can never be non-zero.
B. Magnitude of electric field intensity at a point inside the sphere is directly proportional to the distance of the point from centre of sphere.
C. Magnitude of electric field intensity is directly proportional to `1/r^2` for points outside the sphere where r is the distance of point from the centre of sphere
D. Magnitude of electric field intensity at any point is less than its magnitude on sphere's surface.

Explanation

To solve the problem regarding the electric field due to a solid non-conducting sphere of radius R that is uniformly charged over its volume, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Sphere**:
We have a solid non-conducting sphere of radius \( R \) that is uniformly charged. This means that the charge is distributed evenly throughout the volume of the sphere.

2. **Electric Field Inside the Sphere**:
- For a point inside the sphere at a distance \( r \) from the center (where \( r < R \)), the electric field \( E_{\text{in}} \) can be calculated using Gauss's law.
- The expression for the electric field inside the sphere is given by:
\[ E_{\text{in}} = \frac{kQ}{R^3} r \]
where \( Q \) is the total charge of the sphere, \( k \) is Coulomb's constant, and \( r \) is the distance from the center of the sphere.

3. **Electric Field Outside the Sphere**:
- For a point outside the sphere (where \( r \geq R \)), the sphere can be treated as a point charge located at its center.
- The electric field \( E_{\text{out}} \) at a distance \( r \) from the center is given by:
\[ E_{\text{out}} = \frac{kQ}{r^2} \]

4. **Graphical Representation**:
- The electric field inside the sphere increases linearly with \( r \) (from the center to the surface).
- The electric field outside the sphere decreases with the square of the distance \( r \) (inversely proportional to \( r^2 \)).
- Therefore, the graph of the electric field versus distance \( r \) will show a linear increase up to \( r = R \) and then a decrease as \( r \) increases beyond \( R \).

5. **Key Points**:
- At the center of the sphere, the electric field is zero.
- The maximum electric field occurs at the surface of the sphere.
- The electric field inside the sphere is directly proportional to the distance from the center, while outside it is inversely proportional to the square of the distance.

### Conclusion:
The electric field due to a uniformly charged solid non-conducting sphere varies based on whether the point of observation is inside or outside the sphere. The electric field inside increases linearly with distance from the center, while outside it behaves like that of a point charge, decreasing with the square of the distance.