Fields in Physics assignment question about electron beams in a cathoe ray tube

In summary, the conversation discusses a homework question about calculating the speed of an electron using data from a diagram of a cathode ray tube. The first question involved calculating the kinetic energy gained by the electron and the conversation includes attempts at solving it using different methods. The second equation provided in the conversation includes the charge on the electron, but it is not clear if it is relevant to the problem. The correct solution is found to be 1.87 x 10^7 m/s.
  • #1
bry
2
0

Homework Statement




Ok so we have been given a diagram of a cathoe ray tube, with relevant data on it. The second question asks to "calculate the speed of the electron, using data from the first question". I need to make sure the answer is correct as it leads into many different questions.

I am unable to attach the picture, but here are all details:
Distance between metal plates: 5cm
Length of metal plates: 10cm
Charge on upper plate: 500V
No charge on lower plate
Charge on anode: 1000V


Homework Equations



The first question was to calculate the kinetic energy gained by an electron traveling from cathode to anode. What i calculated was:

E_k=qV=C×V
-1.6×〖10〗^(-19)×1000
E_k=-1.6×〖10〗^(-16) N


The Attempt at a Solution



I used two different methods to work this out, but got two different answers:


F=E_k

E_k=1/2 mv^2

v=√((2×E_k)/m)

v=√((2×-1.6×〖10〗^(-16))/(9.11×〖10〗^(-31) ))

v=-1.87 〖ms〗^(-1)



OR


s=((2×C×V))/m

s=((2×-1.6×〖10〗^(-16)×500))/(9.11×〖10〗^(-31) )

s= -1.76 〖ms〗^(-48)
 
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  • #2
Welcome to PF!
The first speed calc is correct except it works out to 1.87 x 10^7 on my calculator.
I don't understand the second - what is C? I don't recognize the formula.
 
  • #3
Thank you!
I have put it into my calculator again a few times but still getting the same answer: 1.87x10^-24 ... I put it all in separately, so work out what 2x 1.6x10^-16 then divide it...then work out the square root. would doing this alter my answer?

In the second equation the C represents the charge on the electron. I found it on a website so I'm not totally sure it is suitable for this problem.

Also what do i do about the fact that the electron has a negative charge on it? because I'm unable to square root a negative number.
 
  • #4
There is no negative number - the energy is positive. Technically, the polarity is oriented so the V is negative, too, so the qV is positive.

v=√((2×-1.6×10^(-16))/(9.11×10^(-31) ))
Say you separate the numbers and powers: 2x1.6/9.11 = 0.35
The power of 10 is -16-(-31) = 15. So under the square root, 0.35 x 10^15
Square root of that is 1.87 x 10^7.
 
  • #5



As a physicist, I understand your concern for accuracy in your calculations. Based on the given information, I would suggest using the first method to calculate the speed of the electron. The second method, while mathematically correct, may not give an accurate representation of the electron's speed due to the negative value of the result.

Additionally, in the first method, the kinetic energy gained by the electron is equal to the potential energy difference between the anode and the cathode. This potential energy is then converted into kinetic energy as the electron travels from the cathode to the anode.

I would also recommend double checking your units in the first method. The final answer should have units of meters per second (m/s) instead of meters per second squared (m/s^2). Overall, your calculations seem reasonable and I would suggest using the first method to calculate the speed of the electron in this scenario.
 

What is a cathode ray tube?

A cathode ray tube is a vacuum tube that contains an electron gun and a fluorescent screen. It is used to produce images and display information on electronic devices such as televisions and computer monitors.

How does an electron beam work in a cathode ray tube?

The cathode ray tube works by using an electron gun to accelerate electrons towards a fluorescent screen. The electrons are then deflected by electric and magnetic fields to create an image on the screen.

What is the purpose of the magnetic field in a cathode ray tube?

The magnetic field in a cathode ray tube is used to deflect the electron beam, allowing for precise control and manipulation of the image displayed on the screen.

What are the applications of electron beams in cathode ray tubes?

Electron beams in cathode ray tubes are used in various electronic devices, such as televisions, computer monitors, and oscilloscopes. They are also used in scientific research, such as in electron microscopes and particle accelerators.

How are electron beams produced and controlled in a cathode ray tube?

Electron beams are produced by heating a cathode, which releases electrons. These electrons are then accelerated towards the anode by an electric field and are focused into a narrow beam by a series of charged plates. The beam is then controlled by varying the electric and magnetic fields to produce images on the screen.

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