How Does an Electric Field Affect Electron Trajectory in a Cathode Ray Tube?

[penzoate]

Homework Statement

An electron with the kinetic energy of 2.6e-6 Joules is moving to the right along the axis of a cathode ray tube. the length of the cathode ray tube is 16 cm and the length of the deflection inside the cathode ray tube is 4 cm. The electric field = 2e4*N/C. Everywhere else the electric field is zero.
a:) how far is the electron from the axis of the tube when it reaches the end of the plates?
my solution:
Energy =.5*m*v^2 give the initial velocity.

(2*(2e-16 Joules)/(9.11e-31 kg))^.5=v
to find time, I used kinematic equation
x=x(0)+vt --> x-x(0)/v=t --> 16 m/v=t x isthe total length of the cathode ray tube
a=E*q/m(electron)
y=.5*a*t^2

not surehow to find x-component for the velocity, y or time t. Any other variables in this problems I should consider?

Homework Equations

The Attempt at a Solution

 

[Mindscrape]

As I understand the problem the initial velocity is all in the x direction, and then the electric field applied a force to the charge in the y direction. If you know the length of the cathode ray tube, then you can figure out the time. If you know the time you can find how far up it went, how far off the axis it is.

 

[m2003]

I would approach this problem by first identifying the relevant equations and variables. From the given information, we can use the equation for kinetic energy (KE=½mv²) to find the initial velocity of the electron. We can then use the kinematic equation (x=x0+vt) to find the time it takes for the electron to reach the end of the plates.

Next, we can use the equation for electric force (F=qE) to find the acceleration of the electron in the electric field. This can then be used in the kinematic equation (y=½at²) to find the distance (y) the electron is deflected from the axis of the tube.

To find the x-component of the velocity, we can use the equation for uniform circular motion (v=ωr) where ω is the angular velocity and r is the radius of the circular motion. In this case, the electron is moving in a straight line, so the angular velocity is zero and the x-component of the velocity is equal to the total velocity.

Overall, it is important to consider all relevant variables and equations when solving a physics problem, and to carefully organize and label your calculations to avoid mistakes.