Question

The electric field versus distance graph is shown as given. Select the correct statement from the following.
E – electric field, R – radius, r – distance from the centre

• A. The graph shows the variation of the electric field intensity with distance from the centre of a uniformly charged conducting ring of radius R.
• B. The graph shows the variation of the electric field intensity with distance from the centre of a uniformly charged non-conducting solid sphere of radius R.
• C. The graph shows the variation of the electric field intensity with distance from the centre of a uniformly charged conducting solid sphere of radius R.
• D. The graph shows the variation of the electric field intensity with distance from the centre of a uniformly charged non-conducting cylinder of radius R.

Hint:

For a uniformly charged solid sphere: \( E \propto r \) inside and \( E \propto \frac{1}{r^2} \) outside. This is a standard graph pattern.

Answer 1

The Correct Option is B

Step 1: Observe the graph behavior inside the sphere.
From the graph, electric field increases linearly from zero at the centre up to \( r = R \).

Step 2: Recall electric field inside a uniformly charged non-conducting sphere.
Inside such a sphere:
\[ E \propto r \] Hence, electric field increases linearly with distance from centre.

Step 3: Compare with graph.
The given graph shows exactly this linear increase from \( r = 0 \) to \( r = R \).

Step 4: Analyze behavior outside the sphere.
For \( r > R \), electric field decreases with distance as:
\[ E \propto \frac{1}{r^2} \]

Step 5: Compare outer region with graph.
The graph shows a decreasing curve beyond \( r = R \), consistent with inverse square dependence.

Step 6: Reject incorrect options.
- Conducting sphere: electric field inside is zero (not matching graph).
- Ring and cylinder: do not show linear increase from centre.

Step 7: Final Answer.
Thus, the graph represents a uniformly charged non-conducting solid sphere.
\[ \boxed{\text{Option (B)}} \]