Question

A cyclotron accelerates charged particles to high speeds. The particle is injected at a certain velocity, and magnetic fields bend its path into a circle. The cyclotron has a radius of 30m. a) Specify which charged particle you will use in your cyclotron. It could be an electron, a positron, a proton, an antiproton, a deuterium nucleus, or anything else you like. b) Draw a picture of the particle and its path. Set origin and axes. c) Determine a suitable combination of injection velocity and magnetic field strength (with directions). Prove that these achieve the correct radius of circular motion. d) Determine the force on the particle.

Answer 1

The magnetic filed is perpendicular to the page and directed into it.

a +ve charge q ( Proton) is projected into the field at the bottom with a speed v in +x direction

The force on the particle F = q v X B = qvB ( v and B are always perpendicular)

the force on the particle is directed in +y direction at the instant, hence the path of the particle is curved in +y direction

as the particle moves in the magnetic the force on it is always directed perpendicular to B and v

This force only causes a change in direction and do not change the magnitude

v and B are always perpendicular

The particle take a circular path in the magnetic field

The magnetic field provides a centripetal force and

qvB = mv² /r , r is the radius of the circle.

r = qB/mv