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Question #42916
The Question
A conducting liquid drop of mass , radius , and total positive charge is placed inside an elevator that is accelerating upwards with a constant acceleration . A uniform vertical electric field is applied such that the drop is levitated and accelerates exactly with the elevator. Assuming the surface tension is sufficient for the drop to maintain a perfectly spherical shape, what is the difference in surface charge density between the top and the bottom of the drop, ? (Neglect the density of the surrounding air).
Options
- A.
- B.
- C.
- D.
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Step-by-Step Solution
Explanation
How the Examiner Thinks
Intuition_Breaker
Train your brain to resist "obvious" answers that are designed to deceive your intuition.
Concepts Behind This Question
Gauss Law Applicability|Accelerated Frame Hydrostatics|Conductor Interior Potential
Why This Question Is Tricky
Common Mistakes
Students often incorrectly assume that the surface charge distribution on a spherical conductor must remain uniform (), failing to account for the coupling between electrostatic pressure and hydrostatic pressure in an accelerated frame.
The Equivalence Principle dictates an effective gravity , creating a hydrostatic pressure gradient inside the liquid.
To maintain mechanical equilibrium and a spherical shape, the electrostatic pressure must adjust to balance this gradient.
This requires a shift in the surface charge density, which is physically realized by the external electric field needed to levitate the drop.
The problem elegantly rewards students who apply fundamental pressure balance over those who blindly memorize electrostatic formulas.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Electric Charges and Fields - Class 12 |
| Concept | Gauss Law Applicability |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |