# Electron in magnetic field and TV

S.P.P
this isnt homework, im just doing a bit of revision before exams, and came across this problem. Not really sure where to start really. here it is:

In an electron gun of a TV picture tube the electrons (charge -e, mass m) are accelerated by a voltage V. After leaving the electron gun, the electron beam travels a distance D to the screen. In this region there is a transvers magnetic field of maginitude B and no electric field. Show that the approximate deflection of the beam on the screen due to this magnetic field is

d = ((BD^2)/2) * (e/2mV)^0.5

where d is the distance from where the beam would hit the screen if it were traveling straight, to where it does hit the screen.

any ideas?

## Answers and Replies

Meninger
I don't have the equations off the top of my head, however:

You can find the speed of the electron as it leaves the electron gun using the voltage

The change in voltage (the voltage in this case) = the change in kinetic energy divided by the charge of the electron. You have all of the information you need to solve for the velocity.

Voltage=.5(mass of electron)(velocity squared)

YOu should have an equation in which you can solve for the radius of the circular path that the electron would make if it were to travel constantly under the magnetic field. Something like

r=mv/B; something like this. Solve for r.

it seems that my understand of the question might be a little off. Nevertheless you can solve for d through a sine function. But there seems to be no sine function at all in the final equation. Either we are missing some subtle information here or they have found another way solve it or this might require derivatives, something I am not too familiar with. Let me know if you want to know how to do it with a sine function.

Staff Emeritus
Gold Member
Choose axes for the system and write vectors for the velocity and for the magnetic field, then calculate the force. For electrons,

F=(-e)v&times;B

Once you have that, then you have a mechanics problem. Use Newton's second law to calculate the deflection.

S.P.P
hmmm

Im still not gettin it... just cant seem to figure out what to do..

Staff Emeritus
Gold Member
Let the velocity of the electron be v(t), and let the initial velocity be v0=v0i (I have chosen the x axis to lie along the direction of v0. Let the y axis lie along the direction of the magnetic field: B=Bj.

Now:

1. Calculate the force on the electron by: F(t)=(-e)v(t)&times;B
2. Set up Newton's second law: F=m(dv/dt)
3. Solve the differential equation with the initial condition v0=v0i

OK?

S.P.P
ahh

I think i get it, ta