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Question #42672

Difficulty: 8/10 | 🟢 Free

The Question

A smooth horizontal table has a fixed, rough, vertical circular wall of outer radius $R$ . A small block of mass $m$ and charge $-q$ ( $q > 0$ ) is placed on the table, in contact with the outer surface of the wall. Two point charges, each of charge $+Q$ ( $Q > 0$ ), are fixed on the vertical axis passing through the center of the circular wall, at heights $H = \sqrt{3}R$ above and below the table. The coefficient of kinetic friction between the block and the wall is $\mu$ . The block is given an initial tangential velocity $v_0 = \sqrt{\frac{qQ}{32 \pi \epsilon_0 m R}}$ . What is the total distance $s$ traveled by the block along the wall before coming to rest?

Options

A.
$\frac{R \ln 2}{2\mu}$
B.
$\frac{R}{4\mu}$
C.
$\frac{R \ln(1.5)}{2\mu}$
D.
$\frac{R \ln 2}{\mu}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Superposition of Potentials|Angular Momentum conservation|System vs Particle Displacement|Minimum Force to Move a Block

Why This Question Is Tricky

Common Mistakes

This question tests the 'System vs Particle Displacement' trap and the misapplication of the Work-Energy Theorem in the presence of a varying normal force.

Students often incorrectly assume that the conservative electric field does work on the particle, failing to recognize that the displacement is purely tangential while the superposition of the electric fields yields a purely radial force.

Consequently, the electrostatic work is zero.

Furthermore, students frequently misidentify the normal force as a constant $N = F_e$ , ignoring the centrifugal term $-mv^2/R$ required to evaluate the 'flying off' threshold.

By setting up the differential equation with the correct velocity-dependent kinetic friction, the logarithmic dependence of the stopping distance emerges, penalizing any assumption of constant acceleration or incorrect reference frame.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electrostatic Potential and Capacitance - Class 12
Concept	Superposition of Potentials
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free