A beam of electrons moving in the x-direction enters a region where a uniform 208-G magnetic field points in the y-direction. The boundary of the field region is perpendicular to the beam. If the beam penetrates 3.45 mm into the field region, what's the electrons' speed

Explanation:

When a charged particle moves perpendicularly to a magnetic field, the force it experiences is:

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:

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

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,

is the mass of the electron

So, the electron's speed is

i think it'll be 7,000

ok

explanation: