In this experiment we are demonstrating and understanding Faraday’s Law from a practical point of view. We are learning about Faraday’s Law with a hands–on approach. According to Professor Osorno’s notes, Faraday’s Law states that there is an electromagnetic field applied on a wire and that within the wire, the change in the magnetic flux density creates a voltage in the wire. In this experiment we are going to use coils to demonstrate Faraday’s Law, coils are just a wire that is all twirled up. By using a coil, we can actually create a magnetic flux that is better observed in a rounded-up wire rather than a straightened one. We will see if pushing current through the coil will create a voltage within it. The equation for Faraday’s Law is stated below which is:
Where e is the voltage in volts, N is the number of turns in the wire, ϕ is the magnetic flux, and t is the rate of change.
So according to this equation, if we change the magnetic flux we should produce a voltage. Current is flowing through the wire and when we put a magnet in the center we are creating a force that will pull the current towards it. If there is a magnetic force created from putting a magnet into the center, then the rate of change in this case would be to move the magnet around and therefore, changing the intensity of the magnetic force. And according to this equation and what we saw in the lab, if we make bigger changes and did them more frequently, we would get a higher voltage output. This equation also tells us that if we just stick the magnet in there and don’t move it, we won’t get any voltage. That makes sense because if we leave the magnet in there, we will still have a magnetic force being applied, but the force is not changing at all, it is remaining the same throughout, so that means that the rate of change of the magnetic flux is 0, and according to the equation, 0 times any number gives us 0, which is the result, in this case, of the voltage. The equation and the definition basically says everything about Faraday’s Law which is if we want to create a voltage in a coil, we need to apply a magnetic flux in the center and keep that amount of force changing constantly or else we lose our voltage.
Procedure A
1. Build this circuit shown below.
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Circuit 1
2. Use the oscilloscope to view the signal from the circuit.
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Graph 1
This is the graph of the voltage across the coil. As you can see the voltage shown measures 0 because nothing is applied to the coil so the change in magnetic flux is 0 which makes the product voltage equal to 0. Even if there was a magnet in the coil we would still get 0 volts as long as the magnet does not move, and thus, does not produce a changing magnetic flux. So either way we will get no voltage if there is nothing in the coil or if we put a magnet in there, because according to the equation, we need a change in flux, not an applied flux to produce a voltage.
3. Move the magnet around in the center of the coil and observe what happens to the voltage in the oscilloscope.
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Graph 2
In this graph we see that now we are getting a voltage signal because we are moving the magnet in the coil, which makes sense according to the equation. But this voltage will only respond to certain movements. We got this signal because we moved the magnet up and down, but when we moved it in and out of the coil and then side to side nothing happened. So it is very interesting that it will only respond to up and down movement and nothing else. We are also getting a sinusoidal voltage waveform instead of a constant value one.
Procedure B
1. Build the circuit shown below.
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Circuit 2
2. Apply a V(t) = 35cos(377t + ϕ) volts to coil 1.
The 35V is in RMS value so we convert it to about 20VAC. And then we will only use about 10VAC on the circuit. So we apply a voltage of 10.056VAC at 60Hz to the circuit.
3. Use the oscilloscope to measure the voltage produced across both coils, and then find the frequency of the signal.
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Graph 3
This is the graph of the two voltages across both coils. Graph A is the voltage of coil 2 while Graph B is the voltage of coil 1. We can see from here that the voltage of coil 2 is bigger than that of coil 1.
Now we must also find the frequency of the signal, which we can do indirectly from the oscilloscope. Basically we will just measure the period of the waveform and then take the reciprocal, due to the equation, and then we will have the frequency.
The period we found was 16ms by marking points on the oscilloscope and then measuring the distance between the two points.
T = 16ms or 0.016s f = = = 62.5Hz
So our frequency comes out to about 60Hz which makes sense because the input voltage that we gave it was a sinusoid with a frequency of 60Hz, and the frequency needs to remain the same throughout the entire circuit. We cannot have different frequencies in different parts of the circuits, the frequency for the circuit must be the same for the whole circuit.
We did get a frequency that was a bit higher than our input voltage, but that should be fine because we got that probably due to approximation error. It is most likely that we had a percentage error when measuring the period because we were manually doing it and it’s hard to specifically identify the start and end of the period. We only got it based on what we saw but there might have been another start and end point that was closer to our marked points only that we could not see it so accurately. So we did not get an exact approximation of the period which will then mess up the calculated value we get for the frequency because we used the value of the period to calculate the frequency.
Percent Error = × 100% = 4.1667%
4. Insert an iron plunge into the center of the coil and see what happens to the voltage.
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Graph 4
The graph on the previous page is the same as that of graph 3, the only difference is the amplitude of A is bigger than graph 3, other than that the two graphs are similar. This graph was what happened when we put the iron core into the coil, and we also noticed that the more we push the plunge into the coil, the bigger the amplitude of waveform A gets. So basically, the coil will only affect the voltage level of coil 2 where if inserted, it will increase the amplitude of the waveform and the more inserted it is, the more it increases the amplitude. So pushing the whole thing in will make the amplitude rise like crazy and go off the measured charts. And this will only affect waveform A no matter which coil you put the iron plunge in.
Report Questions
1. The signals generated from the oscilloscope are posted in the report and have been indicated and identified.
2. When we move the magnet faster and closer to the coil, the waveform on the oscilloscope fluctuates more, it swings more in amplitude and becomes more visible more often. The frequency will alter a bit with changes made to the magnet motion. It is mostly likely because we are generating a flux from moving the magnet and if we move it faster and closer we are increasing the rate of change. Frequency is the change of something over time and so if the flux is changing, than there will be a frequency and the more the flux changes, the higher the frequency gets. More changes in voltage or anything will result in bigger frequencies. So you could say that frequency is a function of the rate of change of flux, that it is linearly proportional to the change in flux.
3. When we separate the coils and bring them further from each other, the signal decreases and the amplitude of both waveforms dies down to 0. I would assume that the frequency is affected because if separating the coils creates a dying voltage signal that slowly goes to 0, then that means that the more it fades the more it becomes constant at 0, and the more constant it is, the less it changes which means frequency goes down in value since frequency is rate of change. So frequency is affected by the distance where the farther apart they are, the lower the frequency gets.
When we put the coils closer together we get the opposite effect when separating them, which is a bigger signal and an increasing amplitude as well as a well-more developed waveform. This probably happens because there is a magnetic flux within range of the coils so it can make a more improved sine wave. If they are too far away then the effect of the magnetic field is not strong enough to impact the coil when it must travel a farther distance. So distance matter when it comes to magnetism, which is why we get a good, well-developed waveform with higher amplitude, because the two coils are close enough to each other that they can produce a magnetic flux on each other to generate a voltage.
4. Faraday’s Law can be useful in many applications. From procedure A, we can see that Faraday’s Law can be used to design generators. Generators convert mechanical energy into electrical energy, and in that part of the experiment we were moving the magnet to create a voltage. So Faraday’s Law is useful when we want to build a generator; maybe that is one method of how the generator is made.
From procedure B, we could say that Faraday’s Law is helpful because now we know that if we want to amplify a voltage signal across a coil, we just have to put something in the center to create a changing magnetic flux and we will get increased voltage amplitude. This portion of Faraday’s Law can be used as a method to build op-amps, since this part taught us that inserting a center core will boost a signal’s voltage. However, I don’t think this is the method used today to build amplifiers as there can be many problems with this design. It must be relatively big and cannot be made compact to be useful in microelectronic circuits. This method can only create an op-amp of a large size and has no other method of compressing it. The other problem is that the voltage amplitude is increased due to inserting an iron plunge in the center; which means that someone can decrease the voltage and therefore decrease power output just by taking the plunge out. So let’s say that Faraday’s Law was used to build a generator producing electricity for us, so that means that if someone wanted to harm society in this way, that person can just sneak into the power room, take out the iron core inside the machine, and cause a power loss or power shortage to the entire city or area. So these reasons are why I think op-amps are not built with this method today and why generators might not follow this design. But Faraday’s Law can be used to design a generator, only with some improvements and modifications to it such as locking the iron core in so that no one can take it out. But Faraday’s Law is a method to create a voltage from mechanical energy and increase the signal output.
In conclusion, I learned about Faraday’s Law in this experiment. I learned more about Faraday’s Law such as the fact that if we want to create a voltage in a coil, we need a magnetic flux in the center to do so. And we not only need a flux, but we need a rapidly changing one too. So now I know that a constant flux is not good enough to produce a voltage from scratch in a coil, it must be maintained and altered in order to keep the signal up. Just having a flux present isn’t enough to get voltage. This is what Faraday’s Law is all about.
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