Find e/m Ratio: Lab Report Graph Analysis

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In summary, to find the e/m ratio from the gradient of a V vs. I^2 graph, eliminate the magnetic field using the given equations and solve for V. The slope of the resulting linear plot will be equal to e/m times the combined constants of U, R, n, and r.
  • #1
Lorentz09
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Hi all, I'm new to this forum so sorry if this post is a bit scrappy!

Homework Statement



This is part of a lab report I am doing: Plot a graph of V against I^2 and find the e/m ratio from the gradient.

Homework Equations



e/m = 2V/B^2 r^2 where B is magnetic field, r is radius of electron beam

B = U (4/5)^(3/2) nI/R where U is magnetic constant, n is no. of turns per coil, R is radius of Helmholtz coils

The Attempt at a Solution



I'm not sure what exactly to do once I get the gradient!

Many thanks if anyone can help and feel free to ask if I havn't provided enough info :)
 
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  • #2
Note that B is proportional to I and V is proportional to B2 giving V proportioanl to I2. If you plot V vs. I2, the plot is linear and the slope (gradient) of the line is e/m times the other constants. Simply eliminate B using the two given equations and solve for V and the slope term will be evident i.e. V = e/m*K*I2 where K are the combined constants of U, R, n and r.
 

FAQ: Find e/m Ratio: Lab Report Graph Analysis

1. What is the purpose of finding the e/m ratio in a lab report?

The e/m ratio is the ratio of the charge of an electron to its mass. This value is an important physical constant that helps us understand the properties of electrons and their behavior in electric and magnetic fields. By finding the e/m ratio in a lab report, we can verify this important constant and further our understanding of the subatomic world.

2. How is the e/m ratio measured in a lab experiment?

The e/m ratio is typically measured using a cathode ray tube, where a beam of electrons is passed through an electric and magnetic field. By measuring the deflection of the beam in these fields, we can calculate the e/m ratio using known equations and values.

3. What factors can affect the accuracy of the e/m ratio measurement?

The accuracy of the e/m ratio measurement can be affected by various factors such as the strength of the electric and magnetic fields, the quality of the equipment used, and any external interference. It is important to carefully control and calibrate these factors to ensure accurate results.

4. How does the e/m ratio relate to other physical constants?

The e/m ratio is related to other important physical constants such as the speed of light, Planck's constant, and the charge of an electron. These constants are all interdependent and help us understand the fundamental properties of matter and energy.

5. Why is it important to graph the data when finding the e/m ratio?

Graphing the data obtained in the e/m ratio lab experiment allows us to visualize the relationship between the variables (electric and magnetic fields, and electron deflection). This can help us identify any patterns or trends in the data, which can then be used to calculate the e/m ratio with greater accuracy.

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