(a) The electron is moving by circular motion, and the centripetal force that keeps it in the circular path is the magnetic force:
[tex]qvB=m \frac{v^2}{r} [/tex]
where q is the electron charge, v its speed, B the magnetic field intensity (3.50mT = 0.0035 T), and r the radius of the orbit.
By re-arranging the formula, we can write the radius of the orbit as a function of the other variables:
[tex]r= \frac{mv}{qB} [/tex] (1)
We still don't know the velocity of the electron, v, so we can't find the radius yet.
But we can use the angular momentum of the electron, which is:
[tex]L=mvr[/tex]
From which we can rewrite the velocity as
[tex]v= \frac{L}{mr} [/tex] (2)
Substituting (2) into (1), we can now find the radius of the orbit:
[tex]r= \frac{m( \frac{L}{mr}) }{qB} [/tex]
-->
[tex]r= \sqrt{ \frac{L}{qB} } = \sqrt{ \frac{2.5 \cdot 10^{-25 Js}}{(1.6 \cdot 10^{-19}C)(0.0035 T)} }= 0.021 m[/tex]
(b) We can now find the speed of the electron by using equation (2):
[tex]v= \frac{L}{mr}= \frac{2.5 \cdot 10^{-25}Js}{(9.1 \cdot 10^{-31}kg)(0.021 m)} =1.3 \cdot 10^7 m/s [/tex]
