## > Electric charge moving in an electric and a magnetic field

Electric charge moving in an electric (electrostatic) field (velocity being perpendicular to its field lines)

F=qE

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html#c2

Electric charge moving in a magnetic field (velocity being perpendicular to its field lines)

F=qvB

Lorentz force F acts as centripital force and the charge will do a circular motion:

F=Fc <=> qvB=mv2/R <=> R=mv/qB

The radius of the circular motion, termed gyroradius, Larmor radius, or cyclotron radius is given by the above equation.

The angular frequency of this circular motion is known as the gyrofrequency, or cyclotron frequency, and can be expressed as

ω=v/R=qB/m

https://en.wikipedia.org/wiki/Gyroradius

Applications : Cyclotron, Mass Spectrometer

Electric charge moving in an electric and a magnetic field experiences the Lorentz force

https://en.wikipedia.org/wiki/Lorentz_force

F=qE+qvB https://en.wikipedia.org/wiki/Lorentz_force#/media/File:LorentzLeiden2016.jpg