Question

A charged particle is moving perpendicular to a magnetic field in a circle with a radius r. The magnitude of the magnetic field is increased. Compared to the initial radius of the circular path, the radius of the new path is which of the following
1_ larger

2_ smaller

3_equal in size

Answer 1

2_ smaller

The magnitude of the force on the particle is given by the magnetic component of the Lorentz force:

$F_m=qvBsen\theta$

Where is the particle's charge, v its speed, B the magnetic field and $\theta$ is the angle between the particle motion and the magnetic field. According to the Newton's second law, we have:

$F_m=F_c$

Where $F_c$ is the centripetal force, replacing the values of thee forces and solving for r:

$qvBsen\frac{\pi}{2}=m\frac{v^2}{r}\\r=\frac{mv}{qB}$

The radius is inversely proportional to the magnetic field. Therefore, if the magnetic field is increased, the radius of the new path is smaller.