The magnetic force on a charged particle moving at a constant speed in a uniform magnetic field will be doubled when the angle between the velocity of the particle and the direction of the magnetic field changes from 25.0° to
A)57.7°.
B)12.5°.
C)12.2°.
D)50.0°.

Question

Quizplus · Accepted Answer

The magnetic force on 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. To double the force, the sine of the angle must double, since $q$, $v$, and $B$ remain constant. Initially, $\sin(25.0°)$ is involved, and to double this value, you need to find an angle whose sine is twice that of $\sin(25.0°)$. The correct answer is the angle that achieves this doubling effect, which is $57.7°$.

The Magnetic Force on a Charged Particle Moving at a Constant