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PhET Faraday’s Law Simulation

Faraday’s law explains the relationship between coil size, number of windings, rate of change of the magnetic field, and the induced voltage. See how bright you can get the lightbulb to light up by changing different parameters.

Video Transcript

Hello there! Welcome to lecture 25: electromagnetic induction.

Electromagnetic induction is the production of voltage from a changing magnetic field. This property plays a large role in our lives, as it is responsible for the generation of electrical energy and transmission of that energy from power plants to our homes. And as we’ll learn in the next lecture, opens the door to an understanding of electromagnetism.

Each of the following concepts will be discussed in this video: Faraday’s law, generators and motors, transformers, and power distribution and transmission.

Faraday’s law

To recall from lecture 24, it is possible to create magnetism from electricity. Moving charges can create a magnetic field. This is how electromagnets are created.

As it turns out, it’s also possible to generate electricity from magnetism. In this video, I have connected a coil of wire to a galvanometer, which measures electric current. As I move a magnet into the coil of wire, the galvanometer indicates that current is flowing through the circuit.

Whenever there is a moving magnetic field in the vicinity of an electric circuit, that magnetic field will create something called an electromotive force, which produces a voltage. When there is a closed circuit, that voltage will create a current, as we learned in lecture 23. 

Faraday’s law of induction can be used to quantify the strength of this induced voltage. Faraday’s law is a complicated equation, so we will not use the exact equation in this class. Instead, we will learn the qualitative properties of Faraday’s law.

Faraday’s law states that the strength of the induced voltage is proportional to the strength and rate of change of the magnetic field, the number of coils in the wire, and the cross-sectional area of the coil of wire.

In other words, the stronger the magnetic field of the magnet being used, the larger the induced voltage will be. We can see this effect by using a small and large magnet and see how the galvanometer deflects as a result.

The faster the motion of the magnetic field, the larger the induced voltage. When I move the magnet into the coil slowly, the galvanometer registers a small amount of current. When I move the magnet faster, the galvanometer registers a larger amount of current. Note that if the magnetic field does not move, there will be no induced voltage, and therefore no current. Faraday’s law tells us that the magnetic field must be moving with respect to the coil of wire to induce any voltage. If the magnet is held stationary, then the coil of wire can be moved to create this relative motion.

The induced voltage is also proportional to the number of turns and cross-sectional area of the coil of wire. A coil with one or two turns will not experience as much induced voltage as a coil with hundreds or thousands of turns. A coil with a small diameter will have less induced voltage than a coil with a large diameter.

I do not have two coils of wire with identical cross-sectional areas and only differing number of turns, or with the same number of turns and different cross-sectional areas. However, I do have a coil of wire with a small area and fewer turns than another coil, which has a large area and much more turns. As I move the magnet, attempting to keep the speed as constant as possible, through both coils, the current measured by the galvanometer is greater in the larger coil with more turns.

The sign of the induced voltage has to do with three things: which pole, if it is entering or leaving, and which side of the coil it is moving toward or away from. Let’s take a look at how these effects change the sign.

When I move the north pole of the magnet into the right side of the coil, the galvanometer deflects left, which indicates a negative voltage and current. When I switch the magnetic pole and instead move the south pole of the magnet into the right side of the coil, the galvanometer deflects right, which indicates a positive voltage and current.

When I move the north pole of the magnet into the right side of the coil, the galvanometer deflects left. When I instead remove the north pole from the right side of the coil, the galvanometer deflects right, which indicates a positive voltage and current.

When I move the north pole of the magnet into the right side of the coil, the galvanometer deflects left. When I switch sides of the coil and instead move the north pole of the magnet into the left side of the coil, the galvanometer deflects right, which indicates a positive voltage and current.

Note that changing two of these variables simultaneously will cause an effect that cancels itself out. Changing three of these variables simultaneously will cause the current to change its sign from the initial scenario.

Generators and motors

Induction of electric potential in a circuit allows us to create generators. Coal, gas, and nuclear power plants work by heating water into steam. That steam spins a turbine that either moves a magnet around a coil of wire, or moves a coil of wire around a magnet. Wind turbines create this relative movement of a magnet and coil of wire using the power of moving air causing the blades of the generator to rotate. Hydroelectric power plants harness the power of falling water to create this motion.

In this video, I created a generator out of a salad spinner and two coils of wire. Permanent magnets have been placed at regular intervals around the perimeter. When I rotate the salad spinner, the magnetic fields rotate. That rotation causes motion, and when the magnets move around the coils of wire, voltage is generated.

When I connect the output of the generator to a multimeter, we can see the effect of the generator on the average current that is produced. The slower I spin the generator, the smaller the voltage and current that’s generated. The faster I spin the generator, the larger the voltage and current that’s generated. That makes sense based on Faraday’s law of induction.

The voltage created by a generator is AC. As we saw when looking at how the sign of the induced voltage changes in Faraday’s law, having a pole move toward or away from a coil of wire will cause a difference in sign. When the north pole moves toward the coil, the sign will be positive. When the north pole moves away from that same coil, the sign will switch to negative. This process repeats, causing the generation of alternating current. We can see that alternating current by looking at the generator’s output on an oscilloscope.

In sum: a generator is a device that converts mechanical work to electrical energy. The opposite process is also useful. A device that converts electrical energy to mechanical work is known as a motor. We saw an example of a DC motor in lecture 24.

Transformers

A transformer is an electronic device that is capable of transferring energy from a primary circuit to a secondary circuit. It can also change the value of the voltage induced in the secondary circuit compared to the voltage in the primary circuit, either increasing it or decreasing it. This device brings together what we’ve learned in lectures 24 and 25. Electric current flowing through a coil of wire generates a magnetic field. When that current is AC, the electric field changes, which generates a changing magnetic field. That changing magnetic field causes an induced voltage in any coils of wire that are nearby.

Let’s see how this works. In this video, I have two coils of wire located near each other. One of the coils, called the primary, is connected to an AC voltage source. This generates a changing magnetic field in the primary coil. That changing magnetic field is large enough to overlap with the secondary coil, inducing voltage in the secondary coil. We can see that on the galvanometer connected to the secondary. Because the secondary is connected in a complete circuit, current flows. This current is also AC.

While the primary and secondary coils are not physically connected, the effectiveness of the transformer is limited by how far away the two coils are positioned. At a certain point, if the secondary coil moves too far from the primary, the changing magnetic field no longer overlaps with the secondary, and no voltage is induced. This is not a long-distance phenomenon.

It’s possible to increase the effectiveness of this process by placing an iron core into the two coils of wire. This is because the magnetic domains in the iron core will be aligned by the magnetic field generated in the primary. That will cause a further boost to the strength of the magnetic field by increasing how well the primary and secondary devices are coupled together.

When I connect the primary to a DC source, a battery, note that the galvanometer on the secondary no longer deflects. The primary coil is connected properly, as indicated by the glowing light-emitting diode, and the primary therefore generates a magnetic field, but that magnetic field does not change over time. It is static. Faraday’s law of induction tells us that the only way to generate electricity is to have a CHANGING magnetic field. That requirement is not satisfied in this circuit.

Wireless induction can be extremely useful, and today we benefit from technology that uses short-range induction to wirelessly charge our smart phones and other devices.

Transformers aren’t just useful for letting us charge our phones. They are also an essential circuit component that are used for changing the value of voltage between circuits. It is possible to create a step-up transformer, that creates more voltage on the secondary than the primary. It is also possible to create a step-down transformer, that creates less voltage on the secondary than the primary. 

Whether or not a transformer is a step-up or step-down (or if it does not change the voltage at all) has to do with the number of turns of wire in each transformer. In equation form: Vp divided by Np equals Vs divided by Ns. The voltage on the primary divided by the number of turns in the primary coil equals the voltage induced in the secondary divided by the number of turns in the secondary coil.

Let’s say a primary coil has 6000 turns and is powered by a 120 volt AC source. If the secondary coil has 2000 turns, we can calculate the induced voltage on the secondary coil. 120 volts divided by 6000 equals Vs divided by 2000. The voltage on the secondary will be 40 volts. This is a step-down transformer, because the voltage on the secondary is less than the voltage on the primary.

If the primary coil has 500 turns and is powered by a 5 volt AC source, and the secondary coil has 5000 turns, we can calculate the induced voltage. 5 volts divided by 500 equals Vs divided by 5000. The voltage induced on the secondary in this case will be 50 volts. This is a step-up transformer, because the voltage on the secondary is greater than the voltage on the primary.

A step-up transformer sounds pretty great, we’re getting more voltage in the secondary than we had in the primary! At this point, you’re probably very familiar with the law of conservation of energy. The voltage induced in the secondary coil does not come for free. We can use the power equation from lecture 23 to determine what property is affected in the secondary. Power equals current times voltage. Power must be equal in both the primary and the secondary. In other words: Vp times Ip equals Vs times Is. The product of voltage and current in the primary must be equal to the product of voltage and current in the secondary.

If the primary device has a 5 volt AC source, and contains 10 ohms of resistance, then we can use Ohm’s law to calculate the current flow at 0.5 amps. The power consumed by the primary is 5 volts times 0.5 amps: 2.5 watts. The power consumed by the secondary must be 2.5 watts as well. If the voltage generated on the secondary is 50 volts, we can see that the current flowing through the secondary will be limited to 0.05 amps, or 50 milliamps.

When we plug a charging cable into the wall, many times that charging cable is connected to a transformer. As we’ll discuss in the next part of this video, the voltage we have access to in homes in the United States is 120 volts AC. Most modern electrical devices require DC voltage at a much lower value, usually between 5 and 12 volts. 

The large blocky part of our charging cables, colloquially referred to as a “wall wart,” contains a step-down transformer to convert the 120 volts to a smaller value. Then, a rectifier is used to convert that AC voltage to a DC voltage, using a process we discussed in lecture 23. Finally, there is usually some noise-reducing circuitry inside that “wall wart” to ensure that no voltage spikes get through to harm our electronic devices.

While we’ve discussed the transmission process in terms of voltages and coils of wire, in fact, it is the presence of changing electric fields that causes changing magnetic fields, and changing magnetic fields that cause changing electric fields. This induction process does not require the presence of any circuitry to occur. In fact, electromagnetic fields are all around us! While we’ll discuss them in more detail in lecture 26, for now I will conclude this topic by saying that light waves are a manifestation of electromagnetism!

Power distribution and transmission

Now that we’ve learned about how power plants generate electricity, let’s discuss how that electricity gets distributed to our homes!

The process starts at a power plant, most of which generate power using a turbine. Depending on the type of power plant: nuclear, coal, gas, or wind, the power generated by a power plant will be vastly different. As an example, the Byron Nuclear Generating Station in Ogle County, Illinois, has a capacity of approximately two gigawatts. That is: two billion watts of power.

The voltage of the electricity generated by a power plant is typically about 25 thousand volts, 25 kilovolts. The frequency of the AC voltage is 60 hertz in the United States. This voltage is stepped up at the power station to a much larger voltage before being sent through transmission lines on the next phase of its journey to our homes. These are the extremely huge and tall power lines that do not connect to our homes, but instead transmit electricity over long distances.

The voltage through transmission lines vary, but is usually in the neighborhood of 200 to 500 thousand volts. Why is such high voltage used in transmission? Remember that power is conserved. Let’s use the Byron power plant as an example. If two billion watts of power is generated, and that voltage is sent through transmission lines at 200 thousand volts, then the current will be 10 thousand amps. If the voltage was sent through the transmission system at the 25 thousand volts the power plant produced, then the current would be 80 thousand amps. If power is conserved, when voltage increases, current decreases. Current causes heating and losses in the transmission process, so the higher the voltage, the smaller the current, and the more efficient the transmission process will be.

At the end of transmission lines is an electrical substation. At this point, the voltage from the transmission lines is stepped down to approximately 50 thousand volts, and is sent through distribution lines. Distribution lines are smaller and send power from the substation to neighborhoods. These are the power lines you will typically see on the sides of the road in the US. Sometimes they are underground, which prevents power outages from heavy winds and winter storms. Because distribution lines are located in neighborhoods, and only transmit electricity over short distances, the voltage can and should be much lower than what is used in transmission lines.

Transformers on the power poles holding up distribution lines steps down the voltage once more to 240 volts and 120 volts for use in our homes. Note that the frequency of the AC voltage remains 60 hertz throughout its journey, which is why we experience 60 hertz electricity in our homes.

Thanks for taking the time to learn about electromagnetic induction! Until next time, stay well.