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I have made a particle accelerator, like the one in the following image. homemade particle accelerator When a metallic pellet passes through the coil, it lights up and generates a magnetic field described by Biot-Savart's law, by this same Law the direction of the magnetic field $B$ must be tangential, once it finishes passing through the coil, this is deactivated, and the pellet continues its circular orbit. My question is what are the centripetal forces that make the pellet follow its circular orbit, according to me they are the normal forces of the plastic tube.

What is confusing to me is that when I read about cyclotrons, everyone says that the magnetic field after passing over a superconductor is what gives the charged particle centripetal direction, maybe I am confusing the fact that I am only making a model and it turns out which is very different from a real one

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    $\begingroup$ Your model uses plastic pipes to curve the trajectory, but (charged) particles do not follow a circular orbit because they roll in some sort of pipe their trajectory bends thanks to applied magnetic fields. $\endgroup$
    – Quillo
    Commented May 13, 2023 at 20:05
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    $\begingroup$ Nitpick: It's the Biot-Savart law, not "Bio Savart's law". It's named after two people, Jean-Baptiste Biot and Félix Savart. $\endgroup$
    – Hearth
    Commented May 14, 2023 at 5:45
  • $\begingroup$ Well, your model accelerates metal pellets while cyclotrons accelerate electrons or protons or things like that. It's normal that you would curve the metal pellets using things that curve metal pellets (like plastic tubes). If you would try to curve electrons using a plastic tube some would go through the tube and some would chemically react with the tube, but they wouldn't curve, so magnetic fields are needed. $\endgroup$ Commented May 15, 2023 at 13:13

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Yes, in this video the centripetal acceleration is provided by the tube. This is kind of overcomplicated language for "the tube is the only reason the ball follows a circular path." The magnetic coil accelerates the ball because the ball is ferromagnetic - if you put an external magnetic field, the ball is magnetized in such a way that it is attracted to that magnetic field, no matter what direction the field points.

One detail you might have missed is that the coil has to turn off before the ball is done going through it. Ideally, the coil turns off when the ball is in the middle - it has gained all the energy it's going to get from the coil, and if it went any further while the coil was still on, the coil would be pulling back on it.

Particle accelerators accelerate charged particles (which do not experience the same forces as ferromagnetic metal). So magnetic forces do not increase their energy. It is electric fields that accelerate the particles, and magnets, as you say, provide centripetal acceleration. In some sense, the only point of the magnets in particle accelerators, like the tube in this accelerator, is to bring the charged particles back to the "superconducting radiofrequency cavities" that actually increase their energy.

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  • $\begingroup$ I appreciate your answer, however I have an important question. The coil acts as an electromagnet that attracts the pellet, but the field lines of the coil would not be parallel to the tangential velocity and according to Lorentz's law the force would be zero? $\endgroup$ Commented May 13, 2023 at 22:28
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    $\begingroup$ @YAHIRJOSUEOSTOSJIMENEZ yes the field lines are parallel to the ball's velocity. But the ball is not a charged particle - in fact it isn't charged at all. The lorentz force law is not the correct equation to explain the force between the ball and the coil. en.wikipedia.org/wiki/Force_between_magnets I guess the closest thing to the right equation here is $F=\nabla m\cdot B$, but note that $m\propto B$, so the force points toward wherever the field is strongest $\endgroup$
    – AXensen
    Commented May 14, 2023 at 8:27
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A cyclotron is a type of particle accelerator which repeatedly propels a beam of charged particles (protons) in a circular path. Cyclotron uses electromagnetic fields to propel charged particles to very high speeds and energies and is used to produce radioisotopes for a type of medical drugs called radiopharmaceuticals, which diagnose and treat cancer. There are over 1500 cyclotron facilities around the world according to IAEA.

So a cyclotron repeatedly propels particles in a helical path, (not along a circular guide like the plastic tube in your setup, if you constructed it like in the linked Youtube video) achieved by two opposing electromagnets and varying electrostatic field. Charged particles are accelerated outwards from the centre of a flat cylindrical vacuum chamber along a spiral path until they finally land in the bombardment chamber. So in a cyclotron particles are held to a spiral trajectory by a static magnetic field (two electromagnets) and accelerated by a rapidly varying electric field.

In your setup, two electromagnets are used as accelerators, not as guides for the pellet. So pellet is actually guided by the plastic tube along the circular path. A cyclotron, by contrast, uses a magnetic field to bend the trajectories of particles into spiral paths. So basically the setup in the youtube video accelerates the pellets in a two-dimensional path (if you disregard slight deviations due to non-uniform force and gravity) along a circular plastic guide until the setup is turned off manually while the cyclotron accelerates beams of particles in a 3-dimensional vacuum along a helical path until the particle eventually reach and collide in the bombardment chamber.

Diagram of a cyclotron In the above diagram from Wikipedia the electromagnet pole pieces are not shown full size; they must be at least as big as the dees in order to create a uniform field"

As you can see in the diagram above there are no tube-like structures but rather two D-shaped metal hollows with a gap in the middle. The whole device is enclosed in a vacuum chamber. Particles, first released into the middle of the Dees are accelerated through this gap repeatedly. Here is a modified excerpt from Wikipedia that better describes the procedure.

"It (the cyclotron)consists of a pair of "D" shaped sheet metal electrodes called "Dees" placed face to face inside a vacuum chamber, between the poles of an electromagnet. An oscillating radio frequency voltage of several thousand volts is applied to the dees. Atomic particles to be accelerated, such as protons are released in the center. The magnetic field causes them to travel in a spiral path from the centre to the rim of the dees, being accelerated each time they pass from one electrode to the other. When the particles reach the rim they pass out of the dees through a small gap and strike a target."

The device in the linked youtube video is actually an incorrect model of actual cyclotrons. Such a cyclotron model will be highly inefficient for actual particle acceleration as most of the particles' energy will be dissipated by the collision with the wall of the plastic tube.

Inspired by a paper from Norwegian engineer Rolf Wideroe, Ernest Lawrence (1901 – 1958) invented a unique circular particle accelerator, (which he referred to as his "proton merry-go-round" but became better known as "cyclotron") with a pie-shaped concoction of glass, sealing wax, and bronze. A kitchen chair and a wire-coiled clothes tree were also used to make the device work. Ernest Lawrence won the Nobel Prize in 1939 for the invention of the cyclotron. Cyclotrons were the most powerful particle accelerator technology until the 1950s when the synchrotrons superseded them but are still widely used in the field of nuclear medicine and basic research.

Additional note: Coils in the plastic model (model in the linked Youtube video) draw in ferro-magnetic objects like iron pellets and once the objects are drawn in currents to the electromagnetic coils are turned off via an electrical circuit and as pellets have momentum already achieved by prior attraction to the coil, they continue to travel along guided by the walls of the plastic tube. This process is done repeatedly at both coils in order to keep the pellet propelling along. Technically your plastic tube setup will only need one coil with a strong enough magnetic field or a small enough pellet, but adding more coils give better energy efficiency and fewer kinks to the motion of the pellet. (That is if you disregard the energy costs of additional material)

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confus[ed by] the fact that I am only making a model and it turns out which is very different from a real one.

Yes, there are some similarities between the model and the real thing, but also huge differences that are unfortunately "crossed over" between the model and reality:

  • Accelerated thing: iron ball (ferromagnetic, neutral) vs. charged particle.

  • Accelerating force: "pull" from the electromagnet (not Lorentz force!) vs. the electric field (that can both "pull" and "push").

  • Force that holds the thing on its circular path: the normal force of the tube vs. Lorentz force of electromagnets.

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