Protons having kinetic energy K emerge from an accelerator as a narrow beam. The beam is bent by a perpendicular magnetic field so that it just misses a plane target kept at a distance ℓ in front of the accelerator. Find the magnetic field.
Given-
Kinetic energy of proton = K
Distance between the target and the accelerator = l
Therefore, radius of the circular orbit ≤ l
From question it is given that, the beam is bent by a
perpendicular magnetic field, let it be B.
We know-
Now, radius r -
where,
m is the mass of a proton
v= velocity of the particle
B = magnetic force
e= charge on the particle
For a proton, the above equation can be written as-
where r = l
Kinetic energy, K
Substituting the values of v in the equation (1)