# Physics307L:People/Frye/E M ratio

Steve Koch 04:53, 21 December 2010 (EST):Missing is a statistical comparison to the accepted value and a discussion of systematic error.

## Contents

## E over M ratio

This lab was performed in the junior laboratory in the UNM physics building on October 11, and October 18 with Alex Benedict

## Procedure

Inside the sealed bulb is an electron gun and helium gas. The bulb is in the center of Helmholtz coils which produce a magnetic field. A beam of electrons shoots from the gun into the bulb and the magnetic field curves the beam into a circle. We are able to measure the radius of the circle with a ruler on the back of the apparatus. By measuring the radius of curvature as we vary the accelerating voltage of the electron gun and the current supplied to the coils we are able to calculate the ratio of the electron charge(e) over the electron mass(m). According to the equation given on the front of the apparatus:
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle e/m=(2*V)/(B^2*r^2)}**

The idea is that if we know the radius of curvature then we know **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle F/m=a}**
and we know the strength of the magnetic field and the kinetic energy of the electrons we can find the force as a function of the electron charge **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle F=e*vXB}**

We vary the current in the coils to change the magnetic field. We vary the accelerating voltage to change the kinetic energy of the electrons.

## Results

**Trial 1: Constant B field varying accelerating voltage**

average e/m: 2.10899636048x10^11

Standard error of the mean 2.319917067*10^9

relative error 0.20

Fractional Error 0.01

**Trial 2: Constant accelerating voltage varying B field**

average e/m 2.23800140795x10^11

Standard error of the mean 1.453092519x10^9

relative error 0.27

Fractional Error 0.01

Accepted Value C/kg 1.75882017x10^11