Table of Content

Abstract:
The purpose of this experiment was to look at Michael Faraday and Joseph Henry showed in the 1830’s that a changing magnetic field could cause and induced emf electromotive force = voltage in a circuit. Practically, this means that when a copper pick-up coil is placed inside a solenoid whose magnetic field varies with time, current will flow in this coil even if there is no voltage source physically connected to it. This kind of induced emf is seen everywhere in the modern world in the propagation of light and radio waves, in transformers and generators, or in induction coils that give the spark for the car engine. The induced emf is proportional to the number of turns Nc in the “pick-up” coil and is related to the rate of change in the magnetic flux F the pick-up coil. If the magnetic flux F is in units of Webers ,time t in sec, the induced voltage Vemf will be in Volts. For a coil of fixed size, the flux F inside the coil is given by, where B is the intensity of the magnetic field crossing the coil, in Tesla (T), and Ac is the effective cross-sectional area of the coil in square meter (m^2)

For this simple relation to be true the magnetic field has to be perpendicular to the area Ac of the pick-up coil (parallel to the axis of the coil). If the source of the changing magnetic field is a solenoid, a coil that is much longer than it is in diameter, the magnitude of the produced magnetic field inside it is Where Ns is the total number of turns of the solenoid of length ls and I represent the instantaneous.

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Objective:
The objective of this lab was to verify Fraday’s law of induction by measuring the emf generated in a small coil and comparing it with the calculated value; to investigate the relationship between the emf and the frequency of the driving signal.

Procedure:
We have to connect the circuit, then set the function generator output to the triangle signal of amplitude of about 3/4 max. Select the “axial” measurement on the magnetic field probe and press the “Zero” button on the sensor. The axial means the sensor measures the magnetic field along the axis of the probe. We opened the preset experiment file as directed on the whiteboard. The program will record and graph the current in the solenoid remember to calculated from voltage drop across the 10 W resistor, the magnetic field produced inside the solenoid and the voltage induced in the small pick-up coil. Part 1) We had to adjust the frequency of the signal generator to 50 Hz. Place the magnetic field sensor inside the solenoid and then we had to press “Start” to initiate the recording. Make sure the axis of the sensor is always parallel to the axis of the solenoid. Using the “Smart Tool” read the maximum and minimum values of the current and then we calculate the average of these two absolute values. Use this number to calculate the expected magnitude of the corresponding magnetic field of the solenoid (eqn. 3). Compare this value with the one recorded by the magnetic probe again, we have to consider the average of the absolute maximum and minimum. Repeat this procedure for a couple more location of the magnetic field sensor inside the solenoid.

Part 2) We Carefully measure the diameter of the pick-up coil and calculate its cross sectional area. Compare your measured value with the one given in the sample calculation below. Insert the pick-up coil into the solenoid in such way that both axes are parallel. With the magnetic field sensor held next to the pick-up coil inside the solenoid, record the data for different frequencies put out by the signal generator. Suggested values are: 40 Hz, 80 Hz, 120 Hz and 160 Hz. Be aware that because of the alternating current principles the magnitude of the current in the circuit (hence the magnetic field) depends on the frequency. For better results you may want to make some small adjustments in the output signal amplitude to keep the current amplitude constant. In Graphical Analysis make a graph Vemf. meas. (V) vs. frequency f (Hz) and apply linear fit. Is the graph linear? What does that mean?

Part 3) from part 2 we have to look at one should deduce that by increasing the frequency of the current in the solenoid (making the changing magnetic field faster), we can proportionally make the induced emf bigger. Also, an increase in magnetic field (and the magnetic flux) will result in increasing the emf. A common way to increase the magnetic field of a solenoid is to put an iron rod inside it. Conduct such an experiment and comment on the effect. DATA:

Solenoid NS= 550 turns
Coil Nc= 100 turns
t solenoid length Ls = 0.15 m
Diameter of coil D=3.1 cm
0.470 for first step at 40.00
max (0.810), min (-0.823)
after calculating the avg of this two ( avg= 0.8165 A)
3.76e-3 T ( Gamas )
min ( -39.0)
max ( 38.1)
B avg (38.69)

Results:
Linear fit for: data set IV average
Y=mx+b
M(slope): 0.001094 V/HZ
b(Y-intercept); -0.003750 V
Correlation: 0.9998
Rmse: 0.001479
@ 40.00 deltan t (s) 0.0125
@ 80.00 delata t (s) 0.00625
@ 120.00 delata t (s) 0.00416
@ 160.00 delata t (s) 0.00310
Discussion:
To begin, In this experiment we used Computer interface with magnetic field sensor and voltage sensors, function generator, 15 cm solenoid (550 turns),
pick-up coils, 10 power resistor. The measurements were taken through a number of calculations and generated few graph. We had to work on 3 part of process and we got a few calculations and then through the inputting the number we had a Graph shows the data acquired when the other data had entered. From all the data collected above, one can make a good graph of the experiment both suggest that as the height from which the magnet is drop increases the induced emf also increase. On the graph maximum voltage collected increases. So does the minimum voltage with a change in height, this means that the total distance between the two, or in to the words the total emf in height. This happens proportionally as the best fit trend lines suggest. There may have also been human error in reading and entering the correct numbers into the data analysis software Conclusion:

The objective of this experiment was to verify Fraday’s law of induction by measuring the emf generated in a small coil and comparing it with the calculated value; to investigate the relationship between the emf and the frequency of the driving signal. The experiment was little hard because of the info was a lot and it was little hard to follow and the calculation was the main part, but at the end we had correct graphs and correct data.