The electron is accelerated through a potential difference of , so the kinetic energy gained by the electron is equal to its variation of electrical potential energy:
1/2mv²=eΔV
where
m is the electron mass
v is the final speed of the electron
e is the electron charge
is the potential difference
Re-arranging this equation, we can find the speed of the electron before entering the magnetic field:
v=√2eΔv/m=√2(1.6-10-19c)(790v)/9.1-10-31=1.66.10 m/s
Now the electron enters the magnetic field. The Lorentz force provides the centripetal force that keeps the electron in circular orbit:
evb=mv²/r
where B is the intensity of the magnetic field and r is the orbital radius. Since the radius is r=25 cm=0.25 m, we can re-arrange this equation to find B:
b=m/er =3.8.10 t
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