Physics307L F08:People/Le/Notebook/071008

Purpose
We are looking at the ratio of the charge of an electron, to its mass.

Equipment
Uchida e/m Experimental Apparatus, Model TG-13

3 DC power suppies

2 Multimeters



Procedure
Our apparatus is an electron gun, inside a bulb filled with helium, inside a Helmholtz Coil. The electron gun has a metal element that is heated to release electrons, which are then accelerated through an electric field into the bulb. The bulb, filled with the gas, then interacts with these electrons, causing the gas to emit a green light. We can then turn on the Helmholtz Coil to create a magnetic field that is perpendicular to the electron beam, causing a deflection.

We measure the radius of curvature of the beam with a ruler in the background of the bulb. Lining up the right side of the beam with its image in the ruler and vice versa with the left, we can try to eliminate the paralax between the beam and the ruler behind it. We then adjust the strength of the accelerating plates in the gun and the strength of the magnetic field and measure the radii accordingly.

Set 1
B-field constant, change accelerating voltage

set 2
B-field constant, change accelerating voltage

Set 3
B-field constant, change accelerating voltage Changed heater voltage to 6.0 from 6.2

Set 4
B-field changed, constant accelerating voltage

Calculations
To calculate e/m ratio we can use a sum of forces (ignoring gravity) and with Newton's 2nd law and centripetal motion we have

$$F=ma$$

$$qvB=\frac{mv^2}{r}$$

solve for q/m using:

$$qV=\frac{1}{2}mv^2$$

and solving for v and plugging into above

$$\frac{q}{m} = \frac{2V}{B^2 r^2}$$

where $$B=7.8 x 10^{-4} \frac{weber}{amp-meter^2} x I $$