User:Johnny Joe Gonzalez/Notebook/Physics 307L/2009/10/28

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 * style="background-color: #EEE"|[[Image:owwnotebook_icon.png|128px]] E/M
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Safety

 * Check for exposed wires or loose connections as voltages as high as 5kV can be used.
 * Some of the corners on the power supplies are sharp.
 * The electron gun has several components made of glass.

Materials

 * Uchida e/m Experimental Apparatus Model TG-13
 * Two BK Precision Digital Multimeters, Model 2831B
 * Gelman Instrument Company Deluxe Regulated Power Supply
 * SOAR Corporation DC Power Supply Model 7403
 * HP DC Power Supply Model 6384A

Procedure

 * First connect all of the equipment, then turn it all on.
 * The heater for the e/m device will have a voltage reading of 6.3V (as recommended to us by Pranav).
 * The two voltmeters should be set to measure amperes.
 * The E/M apparatus should be set to E/M, this switch is found left of the voltmeter and deflection plate connectors.
 * Once everything is connected and turned on then we wait for about five to ten minutes for the bulb to heat up.
 * Once the bulb is heated then we turn the current adjust knob in order to bend the beam of electrons around the bulb.
 * At this point if the beam forms a helix instead of a circle then try adjusting the bulb to align it until it forms a circle.
 * At this point make a reading of the current, accelerating voltage, left and right measurements off the mirror.
 * The size of the circle can be influenced by several factors: The focus, as this can bring the beam forward or backward on the bulb, the applied current on the Helmholtz coil, and the applied voltage on the electron beam being measured.

data
When taking the data on day on we varied the voltage but kept the current across the coils the same, on day two we varied the current across the coils, while keeping the accelerating voltage the same.

Data Analysis
Using the equation: $$B=\frac{\mu R^{2}NI}{(R^{2}+x^{2})^{\frac{3}{2}}}$$ we can find the B-field, several terms are already given to us for this experiment from the lab manual: R=.15, x^2=R/2, $$\mu =4\pi *10^{-7}$$(the permeability of free space, and N=130(the number of coils on the Helmholtz coils), as well as $$x=\frac{R}{2}$$.

The resulting B value then is shown to be: $$B=7.8*10^{-4}\frac{weber}{Amp*m^{2}}*I$$ From the data above we can then measure the E/M ratio, since we only require the V, I, and radius of the electron beam. I have calculated the different B values below.

However, we still need to relate are measured values with E/M, we can do this by looking at the Lorentz Force: $$F=e(\vec{v}X\vec{B})=m\frac{\vec{v^{2}}}{r}$$, we can then solve for the ratio e/m: $$\frac{e}{m}=\frac{\vec{v}}{r\left|\vec{B} \right|}$$ After which we can relate the velocity to eV: $$\frac{1}{2}mv^{2}=eV\Rightarrow v=\sqrt{\frac{2eV}{m}}$$.

We can then go back to the original equation and substitute v, this gives us the following: $$\frac{e}{m}=\sqrt{\frac{2eV}{m}}\frac{1}{r\left|\vec{B} \right|}\Rightarrow \frac{e^{2}}{m^{2}}=\frac{2eV}{m}\frac{1}{r^{2}B^{2}}\Rightarrow \frac{e}{m}=\frac{2V}{\left(rB \right)^{2}}$$

Now we can use the collected data to discover what the charge-to-mass ratio is.

$$\frac{e}{m}=\frac{2V}{\left(r7.8*10^{-4} \right)^{2}}$$

When V=200: $$\frac{e}{m}=\frac{2*200}{\left(r7.8*10^{-4} \right)^{2}}$$ The data chart below shows the results for e/m with constant accelerating potentials, the current is negative, however, since the negative sign only dictates which direction the current is traveling I used its absolute value for my calculations.

Below is a plot and data for the r^2 vs V plot, click on the chart tab to see the plot



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