A proton and an alpha particle are moving perpendicular to a uniform magnetic field with the same speeds.If the velocity of the proton is at an angle of 20° with respect to the magnetic field direction,at what angle to the magnetic field direction would the alpha particle be moving if it experiences the same magnitude magnetic force as the proton? The alpha particle has 4 times the mass of the proton and twice its charge.
A)10°
B)62°
C)43°
D)9.8°

Question

Quizplus · Accepted Answer

The magnetic force experienced by a charged particle moving in a magnetic field is given by $F = qvB\sin(\theta)$, where $q$ is the charge, $v$ is the velocity, $B$ is the magnetic field strength, and $\theta$ is the angle between the velocity and the magnetic field direction. For the proton and alpha particle to experience the same magnitude of force, and given that the alpha particle has twice the charge of the proton, the sine of the angle for the alpha particle must be half that of the proton to compensate for the double charge. Since the sine function is not linear, we cannot directly halve the angle, but knowing the relationship between charge, force, and angle, we can deduce that the angle for the alpha particle must be smaller and adjust for its greater charge. The correct answer must account for this non-linear relationship, leading to the selection of 9.8°, which is significantly smaller than the proton's angle, reflecting the necessary adjustment for the alpha particle's greater charge and mass, while ensuring the same force magnitude.

A Proton and an Alpha Particle Are Moving Perpendicular to a Uniform