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Question #43866

Difficulty: 8/10 | 🟢 Free

The Question

An electric dipole, consisting of two point charges separated by a rigid massless rod, has a dipole moment of magnitude $p$ and is placed on a rough horizontal surface. A uniform electric field of magnitude $E$ is initially applied parallel to the dipole. The direction of the electric field is then slowly rotated in the horizontal plane. The dipole remains at rest due to static friction until the angle between the electric field and the dipole reaches $\frac{\pi}{3}$ radians, at which point the dipole just begins to slip. At this exact instant, the rotation of the electric field is stopped and its direction is held fixed. Given that the coefficient of kinetic friction between the dipole and the surface is $\frac{1}{\sqrt{3}}$ times the coefficient of static friction, what is the maximum kinetic energy acquired by the dipole during its subsequent motion?

Options

A.
$p E \left( \frac{\sqrt{3} - 1}{2} - \frac{\pi}{12} \right)$
B.
$p E \left( \frac{\sqrt{2} - 1}{2} - \frac{\pi}{24} \right)$
C.
$p E \left( \frac{\sqrt{3} - 1}{2} - \frac{\sqrt{3}\pi}{12} \right)$
D.
$p E \left( \frac{\sqrt{3}}{2} - \frac{\pi}{12} \right)$

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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

Dipole Potential Angular Dependence|Kinetic Friction Transition|Vector Cross-Product

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly model the dynamical transition from static to kinetic friction and apply the Work-Energy Theorem in a rotational context.

A common lethal mistake is assuming that maximum kinetic energy occurs when the dipole fully aligns with the electric field ( $\theta = 0$ ), ignoring that the constant kinetic friction torque will cause deceleration once the electrostatic torque drops below the kinetic friction threshold.

Another frequent trap is using the maximum static friction torque to calculate the dissipative work during the motion, failing to account for the discontinuous drop to kinetic friction immediately after slipping begins.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electrostatic Potential and Capacitance - Class 12
Concept	Dipole Potential Angular Dependence
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free