How can I linearize the equation for q/m in terms of V?

  • Thread starter Thread starter GodsChild086
  • Start date Start date
  • Tags Tags
    Curve
Click For Summary
SUMMARY

The discussion focuses on linearizing the equation for the charge-to-mass ratio (q/m) of an electron in terms of voltage (V) using a cathode ray tube (CRT) experiment. The derived equation is q/m = 2V/B²r², where B represents the magnetic field strength and r the radius. The participant successfully identifies that the relationship can be expressed in the form of a straight line, y = mx, where 2V is the dependent variable and (q/m) is the slope. The participant confirms that the graph should plot 2V on the y-axis against B²r² on the x-axis.

PREREQUISITES
  • Understanding of basic physics concepts, specifically electromagnetism.
  • Familiarity with the cathode ray tube (CRT) and its applications in experiments.
  • Knowledge of linear equations and graphing techniques.
  • Ability to manipulate equations and solve for variables.
NEXT STEPS
  • Study the principles of electromagnetism related to charged particles in magnetic fields.
  • Learn about the applications of cathode ray tubes in modern physics experiments.
  • Explore linear regression techniques for analyzing experimental data.
  • Review the derivation and implications of the charge-to-mass ratio in particle physics.
USEFUL FOR

Students in physics courses, educators teaching electromagnetism, and anyone interested in experimental physics involving charged particles and their properties.

GodsChild086
Messages
22
Reaction score
0
Curve STRAIGHTENING...ARGH!

Yes, curve straightening...every high school student's favorite thing... :confused:

So in my Physics class, our teacher did a demo with the CRT (cathode ray tube) and then he assigned us with the lab exercise. Here are the components of what I'm supposed to include:

Here's the equation presented when Thomson discovered the charge to mass ratio of an electron:

v²/Br = q/m ; where: v = velocity (m/s)
B = magnetic field strength (T)
q = charge on electron (C)
m = mass (kg)
r = radius (m)


Challenge: Find the equation for q/m in terms of V.

Okay, this part I got.

Equations I used:

Ep=Ek
qV = 1/2mv² and the other equation used: v²/Br = q/m
[/color]

Using the first question I solved for v²:

qV = 1/2mv² ; v² = 2qV/m[/color]

My next step taken:

V/Br = q/m ; q²/m² = v²/B²r²

q²/m² = 2qV/mB²r²

Here is the equation for q/m in terms of V:

q/m = 2V/B²r²[/color]

Then we played around with the cathode ray tube, and told us to make a chart. It's for each time he increases the diameter of the circle (beam of electrons), we record the voltage.

This is another challenge he set for us:

Write the equation so that q/m is the slope.

Here's what I did...I'm not sure if I linearized it right (bad grammar...English is not my first language, so I apologize for this).

So I started with this equation again:

q/m = 2V/B²r²[/color]

Equation for a straight line is: y = mx + b

In this case, I don't have a 'b', so it's just y = mx

My equation (to linearize) I came up with is:

y = mx

2V=(q/m)(B²r²) ; where: 2V is the 'y part'
(q/m) is the 'm part' (slope)
and (B²r²) is the 'x part'

After coming up with our equation, he said that make a new table of values. With our new table of values, he said to make a straight-line graph. So my question is (after going through all this mess of typing), is my table going to have a column for 2V and B²r²? As for the graph, is it going to be 2V vs. B²r²? (Where 2V is on the y-axis and B²r² is on the x axis)?
 
Physics news on Phys.org
GodsChild086 said:
So my question is (after going through all this mess of typing), is my table going to have a column for 2V and B²r²? As for the graph, is it going to be 2V vs. B²r²? (Where 2V is on the y-axis and B²r² is on the x axis)?

Well, in a word: yes.

You've already answered your own question haven't you?

GodsChild086 said:
y = mx

2V=(q/m)(B²r²) ; where: 2V is the 'y part'
(q/m) is the 'm part' (slope)
and (B²r²) is the 'x part'
 
I was just wondering if I did everything right...

That's all...cause it seemed complicated at first...
 

Similar threads

  • · Replies 97 ·
4
Replies
97
Views
6K
Replies
12
Views
2K
Replies
20
Views
3K
  • · Replies 29 ·
Replies
29
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
Replies
8
Views
2K
Replies
3
Views
987
Replies
30
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K