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Question #43270

Difficulty: 8/10 | 🟢 Free

The Question

A particle of mass $m$ and charge $+q$ enters the origin $(0,0,0)$ at time $t=0$ with a velocity $\vec{v} = 0.8c \hat{i}$ , where $c$ is the speed of light in vacuum. The region $x > 0$ contains a static uniform magnetic field $\vec{B}_{\text{static}} = B_0 \hat{k}$ and a plane electromagnetic wave propagating in the $+x$ direction. The magnetic field component of the electromagnetic wave is given by $\vec{B}_{\text{wave}} = B_1 \cos(kx - \omega t) \hat{k}$ . If the particle experiences zero initial acceleration at $t=0$ , what is the required value of the static magnetic field $B_0$ ?

Options

A.
$0.25 B_1$
B.
$1.25 B_1$
C.
$-B_1$
D.
$-2.25 B_1$

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

Superposition of Magnetic Fields|Lorentz Force Vector Direction|Particle Velocity vs. Wave Velocity

Why This Question Is Tricky

Common Mistakes

This question tests the superposition principle and the complete Lorentz force law in the presence of an electromagnetic wave.

The primary trap is failing to recognize that an EM wave inherently carries an electric field ( $\vec{E} = \vec{c} \times \vec{B}$ ) which exerts a dominant force on the particle.

Students often incorrectly assume the wave only provides a magnetic field (leading to $B_0 = -B_1$ ) or they account for the wave's electric field but forget to include the wave's magnetic field in the $\vec{v} \times \vec{B}$ term (leading to $B_0 = 1.25 B_1$ ).

The relativistic velocity ensures both electric and magnetic forces are comparable, strictly testing the full vector formulation.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Magnetism and Matter - Class 12
Concept	Superposition of Magnetic Fields
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free