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? Explain.

Answer 1

If charge has $V = \text{const}$ (V-speed) and $V$ is perpendicular to $B$ (B magnetic field), then charge will move by circle trajectory

$$r = \frac{V \cdot m}{q \cdot B}$$

where $V$ – speed

m – mass of charge

q – charge

B – magnetic field

If $r < a \cdot \sqrt{2}$, (where $a$ – side of cubical region) than charge won’t come out from the cubical region.

But if charge has $V$ (V isn’t perpendicular to $B$), then charge will move by spiral trajectory.

Charge will come out from the cubical region.