A charged particle moves through a magnetic field B with a velocity v.

A charged particle moves through a magnetic field B with a velocity v. Which one of the following statements is true for the force (F) experienced by the particle?

[amp_mcq option1=”F is maximum when v and B are parallel to each other.” option2=”F is maximum when v and B are anti-parallel to each other.” option3=”F is maximum when v and B are perpendicular to each other.” option4=”The force F is independent of the angle between v and B.” correct=”option3″]

This question was previously asked in

UPSC CDS-2 – 2023

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The force experienced by a charged particle moving through a magnetic field is given by the Lorentz force formula, F = q(v × B), where q is the charge of the particle, v is its velocity, and B is the magnetic field vector. The magnitude of this force is |F| = |q| |v| |B| sin(θ), where θ is the angle between the velocity vector (v) and the magnetic field vector (B). The force is maximum when sin(θ) is maximum.

The sine function has a maximum value of 1, which occurs when the angle θ is 90 degrees (or π/2 radians). This means the magnetic force is maximum when the velocity of the charged particle is perpendicular to the magnetic field.

When v and B are parallel (θ = 0) or anti-parallel (θ = 180 degrees), sin(θ) = 0, and the magnetic force F is zero. The magnetic force is always perpendicular to both the velocity vector and the magnetic field vector.

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