A proton, a deuteron and an alpha particle, are accelerated through the same potential difference and then subjected to a unifrom magnetic field `vecB`, perpendicular to the direction of their motions. Compare (i) their kinetic energies, and (ii) if the radius of the ciruclar path described by proton is 5 cm, determine the radii of the paths described by deuteron and alpha partcile.

Explanation

To solve the problem step by step, we will analyze the kinetic energy of the particles and the radius of their paths in a magnetic field.

### Step 1: Understanding the Kinetic Energy
When charged particles are accelerated through a potential difference \( V \), their kinetic energy \( KE \) is given by the formula:
\[ KE = qV \]
where \( q \) is the charge of the particle.
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