Electromagnetic Radiation

Introduction:
Antennas are known to transmit electromagnetic radiation and at measurable quantities when provided an alternating voltage source.  This principal behind this is the fact that Maxwell's equations state that a varying electric field (the voltage provided) induces magnetic field lines.  The combination of the two create propagating EM waves.   The voltage signal sent in this wave can be detected and measured.  This lab will explore voltage signal provided by a short antenna and measure the voltage as a function of distance from the detector, an oscilloscope. Assumptions and simplifications made will be discussed in the error/uncertainty analysis of the experiment.

Steps:

A BNC adapter will be used to receive the signal at the oscilloscope.
Simple tests are conducted to verify that the signal at our oscilloscope is generated by the antenna.

1)Check signal at short and far distances as the voltage should fall off as 1/r^3 closely and 1/r and greater distances
2) Vary the frequency at a reasonable distance to detect change in frequency at the oscilloscope.
3) Check close distance signal by varying angles of deflection to verify (sintheta)^2/r^2 voltage variations.

Signal will be minimized at close distance by varying angle of deflection.

Close distance signals fall off as 1/r^3

Data is collected by varying distance from the adapter (measured around its base).

A meter stick is used to approximate 5cm increments.  Signal strength decreases as a function of distance.

Peak to Peak Voltages(Y axis -Volts) as a function of distance(X axis - meters)

A/r fit

A/r^3 fit

A/r^n fit (n=.6)

As we observe, the plotted data fits a more A/r fit.  As long term data collection shows, voltage falls off mostly as A/r.
In this case, are A/r^n resulted in n =.6
The results may differ here because we do no vary at great enough distances to really obtain the A/r relationship of distance and voltage.

Theoretically our voltage may be derived to be



Where L is the length of the antenna, z is the distance from the adapter, and the charge Q is calculated from experimental data.



Distnace (m) Vtheoretical P2P
0
0.05                 0.011631
0.1                   0.005687
0.15                 0.003616
0.2                   0.002704
0.25                 0.002234
0.3                   0.001965
0.35           0.001796

The theoretical peak to peak voltage plot is shown below:

Theoretical peak to peak voltage (V) vs distance (m)

Comparing the graphs above to our theoretical peak to peak voltage, it is clear that experimental data and theoretical agree on the inverse relationship of voltage sensed as a function of distance (z).  Experimental results are not smooth and continuous as theoretical results.  This is caused by the inconsistencies in the inverse power relationship among distance and voltage—experimentally, we will experience a 1/r^3 relationship at close distances and tend towards 1/r at large enough distances.

Measurement Uncertainty:

Peak to Peak Voltage
ΔV = ±1mV

Quantization uncertainty for z:
Δz = ±.01m

accounting for BNC adapter length:
Δz = ±.05m







Questions/Conclusions:

Comparing our experimental results to theoretical we see that there is plenty of room for error given the above equations.  If we compare our theoretical values with experimental, our results agree within the same orders of magnitudes(mostly).
In our model we made several simplifications. We assumed linear charge density. Also, we did not take into account any interference from nearby wires and lab equipment.  We ignored fringing effects of the antenna rod that lead to different electric field distributions.
Future experiments may actually measure current supplied by our voltage generator to improve charge calculations.  Although negligible,  our calculations may also include the energy lost due resistance in the copper antenna.