The electron is accelerated through a potential difference of [tex]\Delta V=780 V[/tex], so the kinetic energy gained by the electron is equal to its variation of electrical potential energy:
[tex] \frac{1}{2}mv^2 = e \Delta V [/tex]
where
m is the electron mass
v is the final speed of the electron
e is the electron charge
[tex]\Delta V[/tex] is the potential difference
Re-arranging this equation, we can find the speed of the electron before entering the magnetic field:
[tex]v= \sqrt{ \frac{2 e \Delta V}{m} } = \sqrt{ \frac{2(1.6 \cdot 10^{-19}C)(780 V)}{9.1 \cdot 10^{-31} kg} }=1.66 \cdot 10^7 m/s [/tex]
Now the electron enters the magnetic field. The Lorentz force provides the centripetal force that keeps the electron in circular orbit:
[tex]evB=m \frac{v^2}{r} [/tex]
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:
[tex]B= \frac{mv}{er}= \frac{(9.1 \cdot 10^{-31}kg)(1.66 \cdot 10^7 m/s)}{(1.6 \cdot 10^{-19}C)(0.25 m)} =3.8 \cdot 10^{-4} T [/tex]
