Data Analysis

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DATA MEASURED:

Trial:    V(volts)    R(m)     I(Amps)   
1 122.3 .0055 2.8
2 122.3 .007 1.87
3 122.3 .0095 1.84
4 239.0 .0055 2.72
5 239.0 .007 1.53
6 239.0 .0095 1.13

 

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Electric Field Values:

 

We must use the equation,B=\mu_onI

Knowing: \mu_o=4\pi\cdot10^{-7}

               n=3620

 

For example:

 B_{Trial\:1}=\mu_onI_{Trial\:1}

B_{Trial\:1}=\:\left(4\pi\cdot10^{-7}\right)\left(3620\right)\left(2.8\right)=.0127  

 

Trial    B Value
1 .0127
2 .0085
3 .0083
4 .0124
5 .0070
6 .0051

 

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 Velocity of Electrons:

 

Before Calculating, the necessary equation must be derived from the following two:

1)Vq=.5mv^2 (note,\:V=voltage\:while\:v=velocity)

This equation equates the kinetic energy gained to the energy added from the electron passing across a potential difference

2)\frac{q}{m}=\frac{v}{BR}

This equation provides the charge to mass ratio in terms the strength of the electric field, its velocity, and the radius of the path it took.

 

We First solve eq. 2 for the mass:

m=\frac{BRq}{v}

And proceed to substitute it directly into equation 1:

Vq=.5\left(\frac{BRq}{v}\right)v^2

Solving for the velocity of the particle, we obtain the result:

v=\frac{2V}{BR}

For example:

v_{Trial\:1}=\frac{2V_{Trial\:1}}{B_{Trial\:1}R_{Trial\:1}}

 

v_{Trial\:1}=\frac{2\left(122.3\right)}{\left(.0127\right)\left(.0055\right)}=3501789\:\frac{m}{s}

Trial     v(m/s)
1 3.502*10^6
2 4.111*10^6
3 3.102*10^6
4 7.009*10^6
5 9.755*10^6
6 9.866*10^6

 

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Mass Calculation:

 

The final piece of the puzzle uses the charge to mass ratio equation we used earlier

\frac{q}{m}=\frac{v}{BR}

But we must first solve it for mass

 m=\frac{BRq}{v}

Now we have all of the necessary data to calculate masses, because we already know the charge of an electron (1.602*10^-19 C)

 

Substituting all of our data for trial 1 yields:

 m_{Trial\:1}=\frac{B_{Trial\:1}R_{Trial\:1}q}{v_{Trial\:1}}

m_{Trial\:1}=\frac{\left(.0127\right)\left(.0055\right)\left(1.602\cdot10^{-19}\right)}{3.502\cdot10^6}

m_{Trial\:1}=3.195\cdot10^{-30}\:kg

Trial     Mass
1 3.195*10^-30
2 2.319*10^-30
3 4.072*10^-30
4 1.559*10^-30
5  8.047*10^-31
6  7.867*10^-31

 

Average Mass: 2.1226\cdot10^{-30}\:kg

Actual Mass: 9.1094\cdot10^{-31}

 

 

Percent Error: \frac{\left(Measured\:Average-Exact\right)}{Exact}\cdot100\%

Percent Error: 133\%

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