If a charged particle is moving through a magnetic field with its velocity at an angle of 45 degrees with respect to the field, what happens to the magnetic force on it if both the speed and magnetic field are doubled?
A) It stays the same.
B) It doubles.
C) It quadruples.
D) It halves.
E) It increases by a factor of 5.66.

Question

Quizplus · Accepted Answer

The magnetic force on a charged particle moving through 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. Doubling both the speed ($v$) and the magnetic field ($B$) results in the force being quadrupled, since $F' = q(2v)(2B)\sin(\theta) = 4qvB\sin(\theta)$.

If a Charged Particle Is Moving Through a Magnetic Field