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*Question:* Suppose that an electron is accelerated from
rest through a voltage
difference of volts and then passes into a region containing a uniform
magnetic field of magnitude T. The electron subsequently executes a
closed circular
orbit in the plane perpendicular to the field. What is the radius of this
orbit? What is the angular frequency of gyration of the electron?

*Answer:* If an electron of mass
kg and charge
C is accelerated
from rest through a potential difference then its final
kinetic energy is

Thus, the final velocity of the electron is given by

The initial direction of motion of the electron is at right-angles
to the direction of the magnetic field, otherwise the orbit of the electron
would be a spiral instead of a closed circle. Thus, we can use Eq. (167)
to calculate the radius of the orbit. We obtain

The angular frequency of gyration of the electron comes from Eq. (168):

** Next:** Example 8.3: Ampère's circuital
** Up:** Magnetism
** Previous:** Example 8.1: Earth's magnetic
Richard Fitzpatrick
2007-07-14