Question

Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field \(E(r)\) and electric potential \(V(r)\) with the distance r from the centre, is best represented by which graph?

Continuous curve stands for intensity. Dotted curve stands for potential.

• A. C
• B. A
• C. D
• D. B

Hint:

Inside a uniformly charged shell the field is zero and the potential is constant; outside both fall with distance.

Answer 1

The Correct Option is C

Step 1: Elimination approach
Check the two curves inside the shell first.

Step 2: Why the other graphs fail
Graphs that show the field rising from zero inside, or a non-zero field inside, contradict Gauss's law.

Step 3: Conclusion
Graph D has zero field and constant potential inside and decaying curves outside, so the answer is option (C).

Final Answer:
Graph D is the correct representation. \[ \boxed{\text{(C) }\text{Graph D}} \]