The purpose of this experiment was to investigate the behavior of EM radiation due to a simple antenna.
Experiment
Set up
Three ways to verify the signal on the oscilloscope is generated by the transmitting antenna:
- Move the wire back and forth to see if there's a change in wave shown in the oscilloscope
- Unplug the detector
- Turn off the function generator
Data:We are measuring the peak to peak amplitude of the
received EM wave as a function of the distance from transmitter.
|
Distance
(m)
|
#
of divisions peak to peak
|
Vertical
scale(mV)
|
Peak
to peak amplitude (mV)
|
|
0
± 0.02
|
3.5
± 0.1
|
50
|
175
± 5
|
|
0.05
± 0.02
|
1.2
± 0.1
|
50
|
60
± 5
|
|
0.10
± 0.02
|
3.2
± 0.1
|
20
|
64
± 5
|
|
0.15
± 0.02
|
2.9
± 0.1
|
20
|
58
± 5
|
|
0.20
± 0.02
|
2.8
± 0.1
|
20
|
56
± 5
|
|
0.25
± 0.02
|
2.4
± 0.1
|
20
|
48
± 5
|
|
0.30
± 0.02
|
2.2
± 0.1
|
20
|
44
± 5
|
|
0.35
± 0.02
|
1.9
± 0.1
|
20
|
38
± 5
|
|
0.40
± 0.02
|
2.0
± 0.1
|
20
|
40
± 5
|
|
0.45
± 0.02
|
1.5
± 0.1
|
20
|
30
± 5
|
|
0.50
± 0.02
|
3.8
± 0.1
|
10
|
38
± 5
|
|
0.55
± 0.02
|
3.6
± 0.1
|
10
|
36
± 5
|
A/r + b plot:
+b.png)
A/r^2 +b plot:
+b.png)
A/r^3 + b plot:
+b.png)
A/r +b plot best fits our data, but our data differed from a 1/r function by a b component because of the approximation used when calculating field near the transmitter. The near field is a function of A/r^3 and far field is a function of A/r.
Theoretical Ananlysis
From the calc variant,
where:
L = 0.1 m
k = 9 * 10^9 N^2 * m^2 / C^2Q = 1.24 * 10^(-10) C
V_0 = 40.29 mV
Therefore,
|
Distance
(m)
|
Theoretical
Amplitude (mV)
|
|
0.05
|
59.99751
|
|
0.1
|
51.0499
|
|
0.15
|
47.61179
|
|
0.2
|
45.82335
|
|
0.25
|
44.73271
|
|
0.3
|
43.99963
|
|
0.35
|
43.47352
|
|
0.4
|
43.07777
|
|
0.45
|
42.76936
|
|
0.5
|
42.52229
|
|
0.55
|
42.31994
|
The experimental and theoretical data have the same trend, but the experimental fluctuate within the theoretical data plot.
Uncertainty
Analysis:
Voltage
uncertainty: ΔV = ± 10 mV (for a scale of
50mV)
= ± 4
mV (for
a scale of 20mV)
= ± 2 mV (for a scale of 10mV)
= ± 2 mV (for a scale of 10mV)
Distance
uncertainty: Δz
= ± 0.001
m (uncertainty of the ruler)
=
+ 0.02
m (detector is not a point and has length involved in measurement )
Total
distance uncertainty: Δztotal
= + 0.021 m / -
0.001 m
Using the uncertainty in distance, we can calculate the theoretical Vmax and Vmin
|
Distance (m)
|
Voltage max (mV)
|
Voltage min (mV)
|
|
0.05 (+0.021/-0.001)
|
60.32
|
54.96
|
|
0.1 (+0.021/-0.001)
|
51.15
|
49.29
|
|
0.15 (+0.021/-0.001)
|
47.66
|
46.74
|
|
0.2 (+0.021/-0.001)
|
45.85
|
45.31
|
|
0.25 (+0.021/-0.001)
|
44.75
|
44.39
|
|
0.3 (+0.021/-0.001)
|
44.01
|
43.76
|
|
0.35 (+0.021/-0.001)
|
43.48
|
43.29
|
|
0.4 (+0.021/-0.001)
|
43.08
|
42.94
|
|
0.45 (+0.021/-0.001)
|
42.77
|
42.66
|
|
0.5 (+0.021/-0.001)
|
42.53
|
42.43
|
|
0.55 (+0.021/-0.001)
|
42.32
|
42.25
|
The experimental graphs does not lie within theoretical with uncertainty.
Discussion:
1. The simplification we made in our model is treating the antenna as a point source but it actually not and it has some length with it. Also, we assume our detector is a point detector but it actually has some length involved in our measurement, too. For example, when we measure the distance from the antenna to the detector is 5 cm, it actually less than 5 cm because of the length of the detector.
2. Maybe improving the model by increasing the distance from the antenna to the detector, so both the antenna ans detector can be treated as a point source.
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