Question

The friends take a few minutes to discuss their ideas. Which of Amy's comments with respect to a charged particle moving in a magnetic field is false? "The magnitude FB of the magnetic force exerted on the particle is proportional to the magnitude of the charge q and to the speed v of the particle." "The magnetic force acting on a charged particle moving in a magnetic field is perpendicular to the particle's velocity." "If the magnetic force is always perpendicular to the velocity, the path of the particle is a straight line." "The work done by the magnetic force on the particle is zero."

Answer 1

Answer:

The statement "if the magnetic force is always perpendicular to the velocity, the path of the particle is a straight line" is false.

Explanation:

The equation for the magnetic force on a charge q moving at velocity v on a magnetic field B is given by the (vectorial) Lorentz Force Law $F=qv\times B$

From it we can clearly see that the magnitude of the magnetic force exerted on the particle is proportional to the magnitude of the charge q and to the speed v of the particle, and that it is also perpendicular to the particle's velocity. This means that at each instant it moves perpendicularly to the force, so the work done by the magnetic force on the particle is zero.

The statement "if the magnetic force is always perpendicular to the velocity, the path of the particle is a straight line" is false not only for this but for any force, a force always perpendicular to a velocity will curve the trajectory.