Experiment 6: Electromagnetic Radiation Lab

PURPOSE: To very and understand the behavior and pattern of EM radiation through a simple antenna

FORMULAS AND DERIVATIONS:

PROCEDURE:

Oscillator shows the signal of the transmitter
Frequency is set to 30kHz

Frequency is set to 30kHz

The transmitter is set at specific lengths away from the receiver. 

Moving the transmitter at different lengths from the receiver showed different oscillations.  

DATA & ANALYSIS:

1. Moving the transmitter close to the receiver creates bigger amplitude on the oscillations.

2. Moving away makes the amplitude smaller.

3. Keeping the transmitter at a constant distance from the receiver does not change the amplitude.

These observations help verify that the oscilloscope is generated by the transmitting antenna. 

Distance (m)	Uncertainty	# of divisions	Uncertainty	Vertical Scale	Amplitude	Uncertainty
0.05	0.03	4.5	0.6	20	90	12
0.1	0.03	2.5	0.6	20	50	12
0.15	0.03	2.8	0.6	10	28	6
0.2	0.03	1.9	0.6	10	19	6
0.25	0.03	3.1	0.6	5	15.5	3
0.3	0.03	2.9	0.6	5	14.5	3
0.35	0.03	2.5	0.6	5	12.5	3
0.4	0.03	2.1	0.6	5	10.5	3
0.45	0.03	1.9	0.6	5	9.5	3
0.5	0.03	1.6	0.6	5	8	3

Amplitude vs. Distance with A/r Linear Fit

Amplitude vs Distance with A/r^2 Linear Fit

The A/r graph had a better fit for the data that was plotted compared to the A/r^2. 

Amplitude vs. Distance with A/r^n Linear Fit

Comparing the new graph of A/r^n to the previous two, this one has a much better linear fit.

Calc Variant:

Using the calculus variant as a method to find the point charge, Q, to help give us the the theoretical V.
Note that Q was assumed to be constant throughout.  

Theoretical Analysis:

The relationship between the voltage and the distance z is approximately the same for both the theoretical values and the values for the maximum amplitude. They both seem to show a A/r^n relationship.

There are slight differences between the theoretical graphs and the maximum amplitude. The theoretical voltage seemed to have slightly higher values in the voltage compared to the maximum amplitude. This pattern holds true for every distance z.

UNCERTAINTY ANALYSIS:

The uncertainty values for the peak to peak voltage are as follows:

±12 for V= (50 mV, 90 mV)

±6 for V= (19 mV, 28 mV)

±3 for V= (7.5 mV, 15.5mV)

The quantization uncertainty in the measurements of the distance z was set to ±0.01 cm. However, this uncertainty distance that was measured may have been calculated to the base of the prong. Consequently , an additional uncertainty, ±.02cm, needs to be added making it a total ∆z uncertainty of ±0.03cm.

Z minimum	Z maximum	Vmax	Vmin	Vuncertainty
0.02	0.08	144.1614372	65.30877	39.42633133
0.07	0.13	71.97213324	44.16668	13.90272463
0.12	0.18	47.28534799	33.06248	7.111432949
0.17	0.23	34.83099292	26.31653	4.257233117
0.22	0.28	27.44228895	21.81686	2.812715339
0.27	0.33	22.59180341	18.61364	1.989079353
0.32	0.38	19.17788295	16.22204	1.477923748
0.37	0.43	16.65045626	14.37048	1.13998933
0.42	0.48	14.706491	12.8957	0.905395224
0.47	0.53	13.16610911	11.6939	0.736106122

CONCLUSION:

Based on the results from the data, the concept of EM radiation can be verified and understood. There were many assumptions that were in constructing the model of the theoretical voltage. The charge, Q, was considered to being a constant value throughout was one assumption that led to a comparable theoretical set of data numbers. The range of error between the two could be explained by discussing the simplifications made in order to keep this experiment simple. Even though we assumed that the linear charge density was constant, there were also other outside interference that could have altered the effects of the radiation that would have given slightly inaccurate data from the oscillator. The assumptions that were made could always be improved by isolating the experiment in an area where there are no other interactions of other EM waves such as cell phones, and even other nearby experiments. Nevertheless, the data between the experimental and the theoretical were all in the range of uncertainty, which helps better verify the experiment and the theory behind EM radiation.