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 solve the problem of finding the specific charge \( \frac{q}{m} \) of the charged particles in a slightly divergent beam that is focused at two successive values of magnetic induction \( B_1 \) and \( B_2 \), we can follow these steps:

### Step 1: Understand the motion of charged particles in a magnetic field
When charged particles move in a magnetic field, they experience a force that causes them to follow a helical path. The radius of this path and the pitch of the helix depend on the charge-to-mass ratio \( \frac{q}{m} \), the magnetic field strength \( B \), and the velocity \( v \) of the particles.

### Step 2: Determine the velocity of the particles
The particles are accelerated by a potential difference \( V \). The kinetic energy gained by the particles is given by:
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