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Question #43774

Difficulty: 8/10 | 🟢 Free

The Question

A particle of rest mass $m_0$ and charge $q$ is projected from the origin with an initial velocity $\vec{v}_0 = \frac{2\sqrt{6}}{5}c \hat{i}$ , where $c$ is the speed of light in vacuum. The region $x > 0$ contains a uniform electric field $\vec{E} = E_0 \hat{j}$ . After a certain time, the particle's velocity vector makes an angle of $45^\circ$ with the x-axis. Neglecting gravity and radiation losses, what is the transverse displacement $y$ of the particle at this instant?

Options

A.
$\frac{2 m_0 c^2}{q E_0}$
B.
$\frac{12 m_0 c^2}{25 q E_0}$
C.
$\frac{12 m_0 c^2}{5 q E_0}$
D.
$\frac{12 m_0 c^2}{q E_0}$

Check Your Answer

Correct Answer

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

Impact Parameter Geometry|Trajectory of Charged Particle|The Velocity-Position Identity

Why This Question Is Tricky

Common Mistakes

This question tests the application of relativistic dynamics and the Work-Energy theorem.

A common trap is assuming that the longitudinal velocity $v_x$ remains constant because there is no force in the x-direction.

In relativity, while the longitudinal momentum $p_x$ is conserved, the continuous increase in transverse momentum $p_y$ increases the particle's total energy and Lorentz factor $\gamma$ .

Consequently, $v_x = p_x / (\gamma m_0)$ must decrease.

Students failing to account for this dynamic inertial resistance will incorrectly apply classical kinematics or assume a constant relativistic mass, leading to erroneous calculations of the transverse displacement.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Atoms - Class 12
Concept	Impact Parameter Geometry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free