Question

A charged particle is fired into a cubical region of space where there is a uniform magnetic field. Outside this region, there is no magnetic field. Is it possible that the particle will remain inside the cubical region? Why or why not?

Short answer

If the charged particle is moving parallel to the magnetic field, then the force is zero, therefore the particle will move straight forward.

Step-by-step solution

When a charged particle enters a uniform magnetic field

If a charged particle is fired into a cubical region of space, where the magnetic field is uniform and there is no magnetic field outside that particular region. Now, a charged particle experiences a force when moving through a magnetic field is given by:

$F=q(v\times B)$

Scenarios arising from a particle entering a magnetic field.

Below are the scenarios that arises from when a particle enters an unform magnetic field.

1. When the particle is moving parallel to the magnetic field and the force is zero the particle will move straight forward.
2. When the particle is moving perpendicular to the magnetic field, the particle will experience a force that will cause the particle to move in a circular motion with a radius R. Now if the diameter of the circular orbit is 2R which is less than the edge of the cube then the particle will remain inside the cubical region.
3. If the particle is moving at an angle of $90°$to the magnetic field then the particle will experience a force that will cause it to move in a helical motion and having a radius of R, hence it will exit the cube at some point even if the diameter of the orbit is less than the edge of the cube.