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, we need to calculate the ratio of the radii of the circular paths described by an alpha particle and a proton when they pass through a magnetic field with the same kinetic energy.

### Step-by-Step Solution:

1. **Understanding the Particles**:
- An alpha particle consists of 2 protons and 2 neutrons, hence it has a charge of \( +2e \) and a mass of approximately \( 4m \) (where \( m \) is the mass of a proton).
- A proton has a charge of \( +e \) and a mass of \( m \).

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