Approximate Maximum Deflection Of Beam

[Melqarthos]

Homework Statement

Estimate the approximate maximum deflection of the electron beam near the center of a CRT television screen due to the Earth's field. Assume the screen is 20 from the electron gun, where the electrons are accelerated by the following voltages. Note that in color TV sets, the beam must be directed accurately to within less than 1 in order to strike the correct phosphor. Because the Earth's field is significant here, mu-metal shields are used to reduce the Earth's field in the CRT.

By 2.2 kV

Homework Equations

We know that

eV=Work
KE=(1/2)mv^2
and |q|vB=(mv^2)/R

The Attempt at a Solution

First I found the speed of the traveling electron(s):

(1.60*10^-19)(2.2*10^3)=(1/2)(9.1*10^-3)(v^2)
v=2.78*10^7

And then when I plug it into the equation

|q|vB=(mv^2)/r

I get a value of deflection to be 3.16 meters, which is not the write answer. I'm not too sure where I went wrong. If anyone could help me out that would be great!

 

[Delphi51]

The 2.2 kV is very low - could it be 22 kV? Is that 20 cm from the screen?
What value did you use for B?

The radius you found is not the answer to the question. This is the situation:

The blue arc is the path of the electron. You are trying to find the red deflection distance marked dx.

If you can write an equation for the circle it will be easy to use it to find dx.

 

[Melqarthos]

Ohh I see :)

I'll be sure to post the answer soon, just need to get down on paper first!

Melqarthos

 

[7tmjw]

whats the answer