If a charged particle (+q) is projected with certain velocity parallel

If a charged particle (+q) is projected with certain velocity parallel to the magnetic field, then it will

[amp_mcq option1=”trace helical path” option2=”trace circular path” option3=”continue its motion without any change” option4=”come to rest instantly” correct=”option3″]

This question was previously asked in

UPSC NDA-1 – 2015

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The correct answer is continue its motion without any change. The magnetic force on a charged particle is given by the Lorentz force formula: F = q(v x B), where q is the charge, v is the velocity vector, and B is the magnetic field vector.

When the velocity vector (v) is parallel to the magnetic field vector (B), the cross product (v x B) is zero. Therefore, the magnetic force (F) on the charged particle is zero. With no force acting on it, the particle will continue to move in a straight line with constant velocity according to Newton’s first law of motion.

A charged particle traces a circular path when its velocity is perpendicular to a uniform magnetic field, and a helical path when its velocity has components both parallel and perpendicular to the field. A magnetic field alone does no work on a charged particle, only changes its direction of motion (unless the velocity is parallel or anti-parallel to the field).

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