Answer:
![1.26\cdot 10^7 m/s](https://tex.z-dn.net/?f=1.26%5Ccdot%2010%5E7%20m%2Fs)
Explanation:
When a charged particle moves perpendicularly to a magnetic field, the force it experiences is:
![F=qvB](https://tex.z-dn.net/?f=F%3DqvB)
where
q is the charge
v is its velocity
B is the strength of the magnetic field
Moreover, the force acts in a direction perpendicular to the motion of the charge, so it acts as a centripetal force; therefore we can write:
![qvB=m\frac{v^2}{r}](https://tex.z-dn.net/?f=qvB%3Dm%5Cfrac%7Bv%5E2%7D%7Br%7D)
where
m is the mass of the particle
r is the radius of the orbit of the particle
The equation can be re-arranges as
![v=\frac{qBr}{m}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7BqBr%7D%7Bm%7D)
where in this problem we have:
is the magnitude of the charge of the electron
is the strength of the magnetic field
The beam penetrates 3.45 mm into the field region: therefore, this is the radius of the orbit,
![r=3.45 mm = 3.45\cdot 10^{-3} m](https://tex.z-dn.net/?f=r%3D3.45%20mm%20%3D%203.45%5Ccdot%2010%5E%7B-3%7D%20m)
is the mass of the electron
So, the electron's speed is
![v=\frac{(1.6\cdot 10^{-19})(208\cdot 10^{-4})(3.45\cdot 10^{-3})}{9.11\cdot 10^{-31}}=1.26\cdot 10^7 m/s](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B%281.6%5Ccdot%2010%5E%7B-19%7D%29%28208%5Ccdot%2010%5E%7B-4%7D%29%283.45%5Ccdot%2010%5E%7B-3%7D%29%7D%7B9.11%5Ccdot%2010%5E%7B-31%7D%7D%3D1.26%5Ccdot%2010%5E7%20m%2Fs)