The gyroradius (also known as radius of gyration or cyclotron radius) defines the radius of the circular motion of a charged particle in the presence of a magnetic field. RADIUS (Remote Authentication Dial In User Service) is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ... In physics, a charged particle is a particle with an electric charge. ... It has been suggested that Magnetic field density be merged into this article or section. ...

Derivation

If the charged particle is moving, then it will experience a Lorentz force given by: In physics, the Lorentz force is the force exerted on a charged particle in an electromagnetic field. ...

Where is the velocity vector, is the magnetic field vector, and q is the particle's electric charge. Notice that the direction of the force is given by the cross product of the velocity and magnetic field. Thus, the Lorentz force will always act perpendicular to the direction of motion, causing the particle to move in a circle (gyrate). The radius of this circle r_g can be determined by equating the magnitude of the Lorentz force to the centripetal force: Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... In mathematics, the cross product is a binary operation on vectors in a three-dimensional Euclidean space. ... Gyration is a company that produces an optical mouse known also as the Gyration. ... An object that moves in a circular path undergoes a continuous acceleration towards the center of the circle. ...

Here m is the particle mass. Solving for r_g, the gyroradius is determined to be: Mass is a property of a physical object that quantifies the amount of matter it contains. ...

Thus, the gyroradius is directly proportional to the particle mass and velocity, and inversely proportional to the particle electric charge, and the magnetic field.

Similarly, the frequency of this circular motion is known as the gyrofrequency, and is given by: Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...

See also

• Cyclotron
• Magnetosphere particle motion

A pair of Dee electrodes with loops of coolant pipes on their surface at the Lawrence Hall of Science. ... // Magnetic Field Lines     The region where magnetic forces can be detected is commonly known as a magnetic field, and similarly the presence of electric forces identifies an electric field. ...

References & further reading