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.
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
A cyclotron accelerates charged particles to high speeds. The particle is injected at a certain velocity,...
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