Final answer:
To determine the specific charge of charged particles accelerated through a potential difference and focused by a magnetic field, the principles of kinetic energy gain and circular motion under magnetic Lorentz force are used, with the specific charge calculated from the balance between these forces.
Step-by-step explanation:
To find the specific charge (charge-to-mass ratio) of the particles, we apply concepts from electromagnetism and mechanics. When the particles are accelerated through a potential difference (V), they gain kinetic energy. Once these charged particles enter the magnetic field (B) of the solenoid, they start moving in a circular path due to the Lorentz force that acts perpendicular to their velocity and the magnetic field.
The radius (r) of this circular path depends on the specific charge of the particle, the magnetic field (B), and the velocity (v) of the particle. The velocity can be determined from the energy gained when the particle is accelerated through the potential difference (V). The kinetic energy (KE) gained by each particle is equal to the charge (q) times the potential difference (V), which is KE = qV. Since KE is also defined as (1/2)mv^2, where m is the mass of the particle, we can solve for the velocity v.
Once the velocity is determined, the radius of the circulation path can be found using the formula r = mv/qB, which is based on the balance between centripetal force and magnetic Lorentz force. Subsequently, by knowing the radius, magnetic field, and potential difference, we can rearrange this equation to solve for the specific charge q/m.