What happens to the velocity of a charged particle moving at any angle with respect to the magnetic field?

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Question: What happens to the velocity of a charged particle moving at any angle with respect to the magnetic field?

Option a: Both the direction and the magnitude of the velocity are changed
- This is not correct because the magnetic force acts perpendicular to the instantaneous velocity and the magnetic field. It does no work on the particle, so it changes direction but not the speed (magnitude) of the velocity. A common misconception is that a magnetic field can change speed, which would require a component of force along the velocity, which magnetic forces do not provide.

Option b: The direction of the velocity remains the same, but the magnitude is changed
- This is incorrect because the velocity vector does not change its magnitude under the influence of a purely magnetic force; the force is always perpendicular to the velocity, which alters the direction but preserves speed. The idea that speed could change would imply work being done by the magnetic field, which cannot happen.

Option c: Both the direction and the magnitude of the velocity remain the same
- This is incorrect because while the magnitude remains constant, the direction is indeed altered. The particle follows a curved path (helical if there is a parallel component) due to the perpendicular magnetic force, so the direction changes.

Option d: The direction of the velocity is changed, but the magnitude remains the same
- This statement correctly captures the physics: the magnetic force causes centripetal acceleration that bends the trajectory, changing the direction of motion, but since the force is always perpendicular to velocity, there is no work done and the speed (magnitude of velocity) stays constant.

In summary, magnetic forces do no work on a moving charge, so they cannot change the kinetic energy or speed; they only change the direction of motion, leading to curved (or helical) paths depending on the component of velocity parallel to B.

UCIC 202503 PHYS101 Quiz 11

What happens to the velocity of a charged particle moving at any angle with respect to the magnetic field?

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