For a uniformly charged non conducting sphere of radius R which of following shows a correct graph between the electric field intensity and the distance from the centre of sphere –

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the electric field intensity (E) around a uniformly charged non-conducting sphere of radius R, we need to analyze the behavior of the electric field both inside and outside the sphere.

### Step-by-Step Solution:

1. **Understanding the Problem**: We have a uniformly charged non-conducting sphere with radius R. We need to determine how the electric field intensity varies with distance from the center of the sphere.

2. **Electric Field Inside the Sphere**:
- For a point inside the uniformly charged non-conducting sphere (where distance \( r < R \)), the electric field intensity \( E \) can be calculated using Gauss's Law.
- The formula for the electric field inside the sphere is given by:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{Q \cdot r}{R^3} \]
where \( Q \) is the total charge of the sphere, \( r \) is the distance from the center, and \( R \) is the radius of the sphere.
- This shows that the electric field inside the sphere is directly proportional to the distance \( r \) from the center.

3. **Electric Field Outside the Sphere**:
- For a point outside the uniformly charged non-conducting sphere (where distance \( r \geq R \)), the electric field behaves as if all the charge were concentrated at the center of the sphere.
- The formula for the electric field outside the sphere is:
\[ E = \frac{1}{4 \pi \epsilon_0} \cdot \frac{Q}{r^2} \]
- This indicates that the electric field outside the sphere is inversely proportional to the square of the distance \( r \).

4. **Graphical Representation**:
- Inside the sphere (for \( r < R \)), the electric field increases linearly with distance from the center.
- At the surface of the sphere (at \( r = R \)), the electric field reaches a maximum value.
- Outside the sphere (for \( r > R \)), the electric field decreases with the square of the distance.

5. **Conclusion**:
- The correct graph would show a linear increase in electric field intensity from the center to the surface of the sphere and then a decrease as we move further away from the sphere.