A narrow beam of protons having kinetic energy K emerges from an accelerator. The beam is deflected by a perpendicular magnetic field such that it just misses a plane target kept at a distance l in front of the accelerator. Determine the magnetic field. (Assume m_p and e represent the mass and charge of a proton, respectively).

Step-by-step solution

The momentum of a proton with kinetic energy K is given by p = 2 m_p K . When the proton beam enters a perpendicular magnetic field B , it follows a circular path of radius R given by: R = p eB = 2 m_p K eB The protons emerge from the accelerator and move towards the plane target. The maximum forward distance traveled by a particle moving in a circular path (starting from the origin and tangent to the initial velocity) is equal to its radius R . For the beam to just miss the plane target kept at a distance l in fro