Shop Windows to the Universe

Hands On Mineral Identification helps you to identify over 14,500 minerals! By M. Darby Dyar, Ph.D. See our DVD collection.

Charged Particle Motion in Earth's Magnetosphere

Charged Particle Motion in a Uniform Magnetic Field

A particle with charge q moving with velocity vector v in a uniform magnetic field vector B experiences a force:

F = qv cross B

The force on the particle is perpendicular to both the velocity and magnetic field and thus does no work on the particle.

Vector diagram of force, velocity, magnetic field for moving charged particle

If the velocity is perpendicular to the magnetic field, the particle moves in a circle of radius r with centripetal acceleration v squared over r. Equating the magnetic force to the particle mass m times the centripetal acceleration, we can show that the radius of gyration (or gyroradius) of the particle is equal to mv over qB.

Click the question marks to see the formulation:

Animation courtesy the COMET and HAO programs at UCAR/NCAR.

For a given gyroradius, the corresponding frequency of gyration (or gyrofrequency), expressed in radians per second, is qB over m.

Click the question marks to see the expression:

Animation courtesy the COMET and HAO programs at UCAR/NCAR.

If a component of the particle's velocity ( v parallel ) is parallel to the magnetic field, then v is replaced by v perpendicular in the preceding two equations, while the v parallel component carries the particle along the magnetic field, creating a helical trajectory.

Animation courtesy the COMET and HAO programs at UCAR/NCAR.

Last modified May 13, 2005 by Randy Russell.

Shop Windows to the Universe Science Store!

Learn about Earth and space science, and have fun while doing it! The games section of our online store includes a climate change card game and the Traveling Nitrogen game!

You might also be interested in:

Cool It! Game

Check out our online store - minerals, fossils, books, activities, jewelry, and household items!...more

Charged Particle Motion in Earth's Magnetosphere

Motions within Earth's metallic core generate the planet's global magnetic field. This magnetic field extends beyond Earth's surface and atmosphere into the space surrounding our home planet. The interaction...more


Altocumulus clouds are part of the Middle Cloud group. They are grayish-white with one part of the cloud darker than the other. Altocumulus clouds usually form in groups. Altocumulus clouds are about...more


Altostratus clouds belong to the Middle Cloud group. An altostratus cloud usually covers the whole sky. The cloud looks gray or blue-gray. The sun or moon may shine through an altostratus cloud, but will...more


Cirrocumulus clouds belong to the High Cloud group. They are small rounded puffs that usually appear in long rows. Cirrocumulus are usually white, but sometimes appear gray. Cirrocumulus clouds are the...more


Cirrostratus clouds belong to the High Cloud group. They are sheetlike thin clouds that usually cover the entire sky. The sun or moon can shine through cirrostratus clouds. When looking at the sun through...more


Cirrus clouds are the most common of the High Cloud group. They are made of ice crystals and have long, thin, wispy streamers. Cirrus clouds are usually white and predict fair weather. ...more


Cumulonimbus clouds belong to the Clouds with Vertical Growth group. They are also known as thunderstorm clouds. A cumulonimbus cloud can grow up to 10km high. At this height, high winds make the top...more

Windows to the Universe, a project of the National Earth Science Teachers Association, is sponsored in part is sponsored in part through grants from federal agencies (NASA and NOAA), and partnerships with affiliated organizations, including the American Geophysical Union, the Howard Hughes Medical Institute, the Earth System Information Partnership, the American Meteorological Society, the National Center for Science Education, and TERC. The American Geophysical Union and the American Geosciences Institute are Windows to the Universe Founding Partners. NESTA welcomes new Institutional Affiliates in support of our ongoing programs, as well as collaborations on new projects. Contact NESTA for more information. NASA ESIP NCSE HHMI AGU AGI AMS NOAA