An `alpha-"particle"` and a proton of the same kinetic energy are in turn allowed to pass through a magnetic field `overset(vec)(B)`, acting normal to the direction of motion of the praricles. Calculate the ratio of radii of the circular paths described by them.

Explanation

To solve the problem of finding the ratio of the radii of the circular paths described by an alpha particle and a proton in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Forces Acting on the Particles**:
When charged particles move through a magnetic field, they experience a magnetic force that acts as a centripetal force, causing them to move in a circular path. The magnetic force \( F \) on a charged particle is given by:
\[
F = qvB
...