A slightly divergent beam of charged particles accelerated by a Potential difference V propogates from a point A along the axis of a solenoid. The beam is brought into focus at a distance l from the point A at two successive values of magnetic induction `B_1 and B_2.` Find the specific charge `q//m` of the particles.

Explanation

To find the specific charge \( \frac{q}{m} \) of the charged particles in the given scenario, we will follow these steps:

### Step 1: Understand the Motion of Charged Particles in a Magnetic Field
When a charged particle moves in a magnetic field, it experiences a magnetic force that causes it to move in a helical path if it has a component of velocity parallel to the magnetic field. The velocity can be broken down into two components: one parallel to the magnetic field (\( v \cos \theta \)) and one perpendicular to it (\( v \sin \theta \)).

### Step 2: Determine the Pitch of the Helical Path
The pitch \( p \) of the helix can be expressed as:
\[
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