Question

A cyclotron with uniform magnetic field , given speed from charged particle and distance from center. Two variable are given solve for the third. Make up a problem with made up numbers and solve show equations on how to get each variable

Answer 1

Cyclotron is a particle accelerator in which the charges particles are accelerated from center to the outward direction in a spriral path. This is done by a setting up a uniform magnetic field and a varying electric field. The particle thus highly accelerated results in the production of high energy beam which is put into use for artificial disintegration etc.

Lorentz force is the combination of both the electric and magnetic force on the moving charged particle. Lets assume a point charge q is moving with velocity v in the region of uniform electric and magnetic fields, then it will experience two forces:

F(electric) = q E

F(magnetic) = q v B

F(lorentz) = F(electric) + F(magnetic)

F(lorentz) = q E + q v B = q ( E + v B)

Hence, F(Lorentz) = q (E + vB)

Under unfirom magnetic field,

F(magnetic) = F(centripital)

q v B = m v^2/R

R = m v / q R