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Question #42257
The Question
Two concentric thin conducting spherical shells have radii and (where is in meters). The inner shell is connected to the ground via a thin conducting wire, while the outer shell is isolated and given a total positive charge (in Coulombs). Let be the magnitude of the electric field just outside the surface of the inner shell, and be the magnitude of the electric field just outside the surface of the outer shell. Determine the dimensionless ratio .
Options
- A.
- B.
0
- C.
3
- D.
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Multi-Concept_Bridge
Master problems that require linking physics and math concepts to solve complex competitive questions.
Concepts Behind This Question
Shell Theorem (Internal vs External)|Conductor Interior Potential|Charged Conducting Sphere
Why This Question Is Tricky
Common Mistakes
This problem targets a classic misapplication of the Shell Theorem.
Students often incorrectly assume that because a uniform spherical shell creates zero electric field in its interior, it has no physical effect on objects inside it.
Consequently, they deduce that grounding the inner shell leaves it uncharged (), leading to the trap answer 0.
The question forces students to distinguish between a zero electric field and a non-zero, constant electric potential.
Grounding sets the total potential to zero, meaning the inner shell must acquire a charge to cancel the constant potential imposed by the outer charged shell.
It also tests the correct application of Gauss's Law for finding the field outside the entire configuration.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Gravitation - Class 11 Part 1 |
| Concept | Shell Theorem (Internal vs External) |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |