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Particles in Magnetic Fields
Storyboard 
Electric charges moving in a magnetic field are deflected perpendicular to the direction in which they move and in which the magnetic field points.
The force acting on the particle depends on the charge, the velocity and the magnetic field is called the Lorentz force.
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Magnitude of the magnetic component of the Lorentz force
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The force ($F$), which generates the magnetic flux density ($B$) on the charge ($q$), moving under a angle between speed and magnetic field ($\theta$) with the speed ($v$), is expressed as:
 $ F = q v B \sin \theta $ |
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Circular motion in magnetic field
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La ecuación de movimiento se deriva del equilibrio entre la fuerza generada por the magnetic flux density ($B$) actuando sobre the charge ($q$) y the particle mass ($m$), que se desplaza con the particle speed ($v$) a the radius ($r$). Esto se expresa mediante la siguiente relación:
| $ m \displaystyle\frac{ v ^2}{ r }= q v B $ |
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Radius of the orbit in the magnetic field
Equation
The orbit at a radius of gyration of particle in magnetic field ($r$) depends on the particle mass ($m$), the speed ($v$), the charge ($Q$), and the magnetic flux density ($B$), and is described by the following relationship:
| $ r =\displaystyle\frac{ m v }{ q B }$ |
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Cyclotron frequency
Equation
The angular Speed ($\omega$) is derived from the charge ($q$), the magnetic flux density ($B$), and the particle mass ($m$), using the following relationship:
| $ \omega =\displaystyle\frac{ q B }{ m }$ |
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Video
Video: Particle dynamics