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p = v para T .

The result is a helical motion    , as shown in the following figure.

An illustration of a positively charged particle moving in a uniform magnetic field. The field is in the positive x direction. The initial velocity is shown as having a component, v sub para, in the positive x direction and another component, v sub perp, in the positive y direction. The particle moves in a helix that loops in the y z plane (counterclockwise from the particle’s perspective) and advances in the positive x direction.
A charged particle moving with a velocity not in the same direction as the magnetic field. The velocity component perpendicular to the magnetic field creates circular motion, whereas the component of the velocity parallel to the field moves the particle along a straight line. The pitch is the horizontal distance between two consecutive circles. The resulting motion is helical.

While the charged particle travels in a helical path, it may enter a region where the magnetic field is not uniform. In particular, suppose a particle travels from a region of strong magnetic field to a region of weaker field, then back to a region of stronger field. The particle may reflect back before entering the stronger magnetic field region. This is similar to a wave on a string traveling from a very light, thin string to a hard wall and reflecting backward. If the reflection happens at both ends, the particle is trapped in a so-called magnetic bottle.

Trapped particles in magnetic fields are found in the Van Allen radiation belts around Earth, which are part of Earth’s magnetic field. These belts were discovered by James Van Allen while trying to measure the flux of cosmic rays    on Earth (high-energy particles that come from outside the solar system) to see whether this was similar to the flux measured on Earth. Van Allen found that due to the contribution of particles trapped in Earth’s magnetic field, the flux was much higher on Earth than in outer space. Aurorae , like the famous aurora borealis (northern lights) in the Northern Hemisphere ( [link] ), are beautiful displays of light emitted as ions recombine with electrons entering the atmosphere as they spiral along magnetic field lines. (The ions are primarily oxygen and nitrogen atoms that are initially ionized by collisions with energetic particles in Earth’s atmosphere.) Aurorae have also been observed on other planets, such as Jupiter and Saturn.

Figure a is an illustration of the Van Allen radiation belts. Charged particles move in helices parallel to the field lines and trapped between them. Figure b is a photograph of the aurora borealis.
(a) The Van Allen radiation belts around Earth trap ions produced by cosmic rays striking Earth’s atmosphere. (b) The magnificent spectacle of the aurora borealis, or northern lights, glows in the northern sky above Bear Lake near Eielson Air Force Base, Alaska. Shaped by Earth’s magnetic field, this light is produced by glowing molecules and ions of oxygen and nitrogen. (credit b: modification of work by USAF Senior Airman Joshua Strang)

Beam deflector

A research group is investigating short-lived radioactive isotopes. They need to design a way to transport alpha-particles (helium nuclei) from where they are made to a place where they will collide with another material to form an isotope. The beam of alpha-particles ( m = 6.64 × 10 −27 kg, q = 3.2 × 10 −19 C ) bends through a 90-degree region with a uniform magnetic field of 0.050 T ( [link] ). (a) In what direction should the magnetic field be applied? (b) How much time does it take the alpha-particles to traverse the uniform magnetic field region?

An illustration of the proposed device. Alpha particles enter the bottom of an evacuated pipe, moving upward. The pipe makes a 90 degree bend, radius r, to the left, then continues horizontally. The particle beam exits to the left. The bend is in a region with uniform magnetic field.
Top view of the beam deflector setup.
Practice Key Terms 2

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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