# Motion Of An Electron In A Magnetic Field

Author:
Alkis
This material has been created for the GeoGebra 20-20 Stem Challenge. Introduction An electron placed in a uniform electric field experiences a constant force that accelerates the electron to a final velocity. Following this, if the accelerated electron enters a homogeneous magnetic field it experiences the Lorenz force which acts perpendicular to the velocity. Under the appropriate conditions, namely when the electron velocity is perpendicular to the magnetic field direction,Lorenz force acts as a centripetal force that leads to circular motion of radius R. The value of the radius depends on the values of the accelerating voltage and the magnetic field. Furthermore the circular frequency of the electron trajectory depends on the strength of the magnetic field. In the physics lab we generate the homogeneous electric field using a planar capacitor and the homogeneous magnetic field using a coil (Helmhotz coil) connected to a dc electric source. More can information be found in the http://physicslab.geogebra.gr/ website.
In the Geogebra file we show the electron trajectory in a a magnetic field (B) that is produced by the electric current (I). We can vary the values of the capacitor voltage V and current intensity I using two sliders.One can observe that increasing the capacitor voltage the radius of the electron increases, while increasing the current intensity (I), the intensity (B) of the magnetic field increases and the radius decreases. Careful observation also shows that as the intensity B increases the circular frequency of the electron motion increases too. For visualization purposes, the circular frequency which is enormous, in reality, haw been scaled down by a factor of 1000000000000.